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A  COMPLETE  COURSE  IN  GERMAN. 

By  JAMES  H.  WORMAN,  AM. 

EMBRACTXO 

ELEMENTARY    GERMAN    GRAMMAR, 

COMPLETE    GERMAN    GRAMMAR, 

COLLEGIATE    GERMAN    READER, 
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explains,  first,  the  conditions  and  processes  by  which  the  mind  receives  ideas,  and 
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^.     /&,    /f  >•-  >0 


A  MANUAL 

OP   THE   PRINCIPLES  AND  PRACTICE   OF 

ROAD-MAKING 

COMPRISING  THE 
LOCATION,  CONSTRUCTION,  AND  IMPROVEMENT 

OF 

ROADS, 

(COMMON,  MACADAM,  PAVED,  PLANK,  ETC,,) 

AND 

RAIL-ROADS. 

• 

BY   W.  M.    GILLESPIE,  LL.D.,   C.E. 

TENTH      EDITION,     WITH      LARGE      ADDENDA. 
EDITED   BT 

CADY  STALEY,  A.M.,  C.B. 


"  Every  judicioiu  improvement  in  the  establishment  of  Road*  and  Bridget  infreaia  On 
taliu  of  land,  enhance  the  price  of  commodities,  and  augment*  the  public  wealth." 

DB  WITT  CUICTC& 


A.    S.    BARNES    &    COMPANY, 

NEW  YORK  AFD  CHICAGO. 

JOHfM  S.  PRELL 

Civil  &  Mechanical  Engineer. 

SAN  FRANCISCO,  CAL. 


Entered  according  to  Act  of  Congress,  in  the  year  1871,  by 

A.    8.    BARNES    &    CO., 
IB  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


Engineering 
Library 

TE- 
JOHN  S.  PRELL 

Qott  &  Mechanical  Engineer. G 

SAN  FRANCISCO,  CAL. 
PREFACE. 


mon  roads..of  the  United  States  are  inferio-  to  thost 
rf  any  other  civilized  country.  Their  faults  are  those  of  direc- 
tion, of  slopes,  of  shape,  of  surface,  and  generally  of  defi- 
ciency in  all  the  attributes  of  good  roads.  Some  of  these 
defects  are  indeed  the  unavoidable  results  of  the  scantiness 
of  capital  and  of  labor  in  a  new  country,  but  most  of  them  arise 
from  an  ignorance  either  of  the  true  principles  of  road-making, 
or  of  the  advantages  of  putting  these  principles  into  prac 
tice.  They  may  therefore  be  removed  by  a  more  general  diffu- 
sion of  scientific  instruction  upon  this  subject,  and  to  assist  in 
bringing  about  this  consummation  is  the  object-of  the  present 
volume.  In  it  the  author  has  endeavored  to  combine,  in  a 
systematic  and  symmetrical  form,  the  results  of  an  engineer- 
ing experience  in  all  parts  of  the  United  States,  and  of  an 
examination  of  the  great  roads  of  Europe,  with  a  careful  di- 
gestion of  all  accessible  authorities,  an  important  portion  of 
the  matter  having  never  before  appeared  in  English.  He  has 
striven  to  reconcile  the  many  contradictory  theories  and 
practices  of  road-making  ;  to  select  from  them  those  which 
are  most  in  accordance  with  the  teachings  of  science ;  to 
present  as  clearly  and  precisely  as  possible  the  leading  fea- 
tures of  those  approved,  laying  particular  stress  on  such  as 
are  most  often  violated  or  neglected  ;  and  to  harmonize  the 
successful  but  empirical  practice  of  the  English  engineers 
with  the  theoretical  but  elegant  deductions  of  the  French. 


713877 


Sngineering 
Library 


4  PREFACE. 

Before  the  construction  of  a  road  is  commenced,  its  makers 
should  well  determine  "  What  it  ought  to  be,"  in  the  vital 
points  of  direction,  slopes,  shape,  surface  and  cost.  This  is 
therefore  the  first  topic  discussed  in  this  volume.  The  next 
is  the  "  Location"  of  the  road,  or  the  choice  of  the  ground 
over  which  it  should  pass,  that  it  may  fulfil  the  desired 
conditions.  In  this  chapter  are  given  methods  of  perform, 
ing  all  the  necessary  measurements  of  distances,  directions 
and  heights,  without  the  use  of  any  instruments  but  such  as 
any  mechanic  can  make,  and  any  farmer  use.  The  "  Con- 
struction" of  the  road  is  next  explained  in  its  details  of  Exca- 
vation, Embankment,  Bridges,  Culverts,  &c.  At  this  stage 
of  progress  our  road-makers  too  generally  stop  short,  but  the 
road  should  not  be  considered  complete  till  "  The  Improve 
ment  of  its  surface"  has  been  carried  to  as  high  a  degree  of 
perfection  as  the  funds  of  the  work  will  permit.  Under  this 
head  are  examined  earth,  gravel,  McAdam,  paved,  plank  and 
other  roads.  "  Rail-roads,"  and  their  motive  powers,  are 
treated  of  in  the  next  chapter.  The  "  Management  of  town 
roads"  is  last  taken  up,  the  evils  of  the  present  system  of 
Road-tax  are  shown,  and  a  better  system  is  suggested.  In 
the  "  Appendix"  are  minute  and  practical  examples  of  the 
calculations  of  Excavation  and  Embankment. 

To  enable  this  volume  the  better  to  attain  its  aim  of  being 
doubly  useful,  as  a  popular  guide  for  the  farmer  in  improving 
the  roads  in  his  neighborhood,  and  as  a  College  Text  book, 
intioductory  to  the  general  study  of  Civil  Engineering,  the 
mathematical  investigations  and  professional  details  have  been 
printed  in  smaller  type,  so  as  to  be  readily  passed  over  bv 
thr  unscientific  reader. 

NOTE.—  The  addition?  In  this  edition  of  the  MANUAL  or  ROADS  AND  RAIL 
BOADH,  »re  from  the  notes  of  the  author's  lectures  to  the  Civil  Enfiineei  iiiy 
vU*«  Jn  Union  College.  C.  8. 


AUTHORITIES  REFERRED  TO. 


Alexander.    Amer.  Ed.  of  Simms  on  Levelling,  Baltimore,  1837. 

Annales  des  Fonts  et  Chaussees,  Paris. 

Anselin.     Experiences  sur  la  main-d'ceuvre  des  differens  travaux,  Parii 

Babbage.     Economy  of  Machinery  and  Manufactures,  London,  1831. 

Berthault-Ducraux.     De  1'Art  d'entretenir  les  Routes,  Paris,  1837. 

Bloodgood.    Treatise  on  Roads,  Albany,  1838. 

Chevalier.     Les  voies  de  communication  aux  Etats  Unis,  Paris,  1843 

Civil  Engineers'  and  Architects'  Journal,  London. 

Cresy.    Encyclopedia  of  Civil  Engineering,  London,  1847. 

Davies.     Elements  of  Surveying,  &c.,  New  York,  1845. 

Delaistre.     La  Science  des  Ingenieurs,  Paris,  1825. 

Dupin.     Applications  de  Geometric,  Paris,  1822. 

"         Travaux  civils  de  la  Grande  Bretagne,  Paris,  1824. 
Eaton.     Surveying  and  Engineering,  Troy. 
Edgeworth.     Construction  of  Roads  and  Carriages. 
Flachat  $•  Bonnet.     Manuel  et  Code  des  Routes  et  Chaussees,  Paris. 
Frame.     Trigonometrical  Surveying,  London,  1840. 
Gayffier.     Manuel  des  Ponts  et  Chausse'es,  Paris,  1844. 
Gerstner.     Memoire  sur  les  grandes  routes,  Paris,  1827. 
Grieg.     Strictures  on  Road-police,  London. 
Griffith.     On  Roads,  London. 
Hughes      Making  and  Repairing  Roads,  London. 
Journal  de  1'Ecole  Polytechuiqne,  Paris. 
Journal  of  the  Franklin  Institute,  Philadelphia. 
Jullien.     Manuel  de  1'Ingenieur  Civil,  Pans,  1845. 
Laws  of  Excavation  and  Embankment  on  Railways,  London,  1840. 
Le count.     Treatise  on  Railways,  London,  1839. 

Macneill.    Tables  for  calculating  Cubic  quantities  of  Earthwork,  Loudoa 
Mahan.     Course  of  Civil  Engineering,  New  York,  1846. 
Marlette.     Manuel  de  1'Agent-voyer,  "aris,  1842. 
McAdam.     System  of  Road-Making,  London,  1825 


6  AUTHORITIES. 

Millington     Civil  Engineering,  Philadelphia,  1839. 

Morin.    Aide-Memoire  de  Mecanique,  Paris,  1843. 

Mosely.    Mech  principles  of  Engineering  and  Architecture,  London,  1843 

Navier.    Travanx  d'entretien  des  Routes,  Paris,  1835. 

"          Application  de  la  M6canique  aux  constructions,  Paris. 
Nimmo.     On  Roads  of  Ireland,  &c. 
Parnell.    Treatise  on  Roads,  London,  1838. 

Paterson.    Practical  Treatise  on  Public  Roads,  &c.,  Montrose,  1820. 
Penfold.    On  Making  and  Repairing  Roads,  London,  1835. 
Poncelet.     Mecanique  Industrielle,  Paris,  1841. 
Potter.    Applications  of  Science  to  the  Arts,  New  York,  1847. 
Railroad  Journal,  New  York,  1832-1847. 
Renwick.     Practical  Mechanics,  New  York,  1840. 
Reports  of  U.  S.  Commissioner  of  Patents,  Washington. 
Reports  of  U.  S.  Engineer  Corps,  Washington. 
Reports  to  Parliament  on  Holyhead  roads,  &c.,  London. 
Ritchie*    Railways,  London,  1846. 
Road  Act  of  New  York,  Rochester,  1845. 
Roads  and  Railroads,  London,  1839. 
Sganzin.    Course  of  Civil  Engineering,  Boston,  1837. 

"          Coure  de  Construction  par  Reibell,  Paris,  1842. 
Simma.    Telford's  rules  for  making  and  repairing  roads,  London 

"          Public  Works  of  Great  Britain,  London. 

"          Sectio-Plauography,  London. 

Stevenson.    Civil  Engineering  of  North  America,  Lor.  don,  183& 
Telford.     Reports  on  Holyhead  roads,  L  nidon. 
Tredgold.    On  Railroads,  Londor,  1635. 
U'oocf.    On  Railroads,  Philadelph  a,  1333- 


ANALYTICAL  TABLE  OF  CONTENTS. 


PAOB 

INTRODUCTION ...    ..  15 

CHAPTER  I.— WHAT  ROADS  OUGHT  TO  BE-.  25 

1.  AS  TO  THEIR  DIRECTION 20 

Importance  of  straightness ib 

Advantages  of  curving ib. 

Pleasure  drives 30 

2.  AS  TO  THEIR  SLOPES , 32 

Loss  of  power  on  inclinations ib 

Undulating  roads 37 

Greatest  allowable  slope 38 

Considered  as  a  descent .4 

"  an  ascent 40 

Least  allowable  slope 43 

Tables  of  corresponding  slopes  and  angles 41 

3.  AS  TO  THEIR  CROSS-SECTION 45 

Width ib. 

Shape  of  the  road-bed 48 

Foot-paths,  &c 53 

Ditches ib 

Side-slopes  of  the  cuttings  and  filings 55 

4.  AS  TO  THEIR  SURFACE 58 

Qualities  to  besought ib. 

Smoothness  and  hardness ift 

Resistances  to  be  lessened ib. 

Elasticity ib. 

Collision 59 

Friction     60 


8  CONTENTS. 

PAO* 

5.  AS  TO  THEIR  COST 65 

Comparison  of  cost  and  revenue io 

Amount  of  Traffic 66 

Cost  of  its  transportation ib. 

Profit  of  improving  the  surface 67 

"       "  lessening  the  length 68 

"       "  avoiding  a  hill ib, 

Consequent  increase  of  travel 70 

CHAPTER  II.— THE  LOCATION  OF  ROADS 72 

1.  ARRANGEMENT  OF  HILLS.  VALLEYS  AND  WATER- 

COURSES 74 

Line  of  greatest  slope 75 

Inferences  from  the  water-courses 78 

2.  RECONNAISSANCE 81 

3.  SURVEY  OF  A  LINE 80 

Measurement  of  distances-. 87 

"              directions. 90 

"               heights 93 

4.  MAPPING  THE  SURVEY 101 

Plot  of  the  distances  and  directions. ib. 

Profile  of  the  distances  and  heights. 103 

5.  ESTABLISHING  THE  GRADES 105 

6.  CALCULATING  EXCAVATION  AND  EMBANKMENT    112 

Preliminary  arrangements 113 

Sectio-rianography it. 

Tabular  entries 115 

Cauical  contents. 117 

Balancing  the  excavation  and  embankment 118 

Shrinkage ib. 

Change  of  grade 119 

Transverse  balancing 122 

Distances  of  Transport 123 

7«  ESTDMATE  OF  THE  COST 124 

Earthwork ib. 

Wages. ib. 

duality 125 

Distance 127 

Und,  Bridge*,  &c. 132 


CONTENTS.  9 

PAU« 

8.    FINAL  LOCATION  OF  THE  LINE 134 

Rectification 135 

Curves. 137 

Circular  arcs 138 

Parabolic  arcs 143 

Setting  grade  pegs 145 


CHAPTER  III.— CONSTRUCTION  OF  ROADS- -147 

1.  EARTHWORK ...  149 

Problems  on  removing  earth ib. 

Excavation 154 

Loosening ib. 

Scraper  or  scoop 155 

Barrow  wheeling 156 

Carts,  etc 158 

Deep  cuttings 159 

Spoil  banks. . 160 

Side-slopes tb. 

Tunnelling 161 

Blasting ib. 

Embankments 165 

Formation  of  banks ib. 

Protection  of  slopes 167 

Swamps  and  bogs , 163 

Side-hills 160 

Trimming  and  shaping 171 

2.  MECHANICAL  STRUCTURES 173 

Bridges ib. 

Culverts  and  drains 178 

Catchwaters,  or  Water-tables 180 

Retaining  Walls 182 


CHAPTER    IV.— IMPROVEMENT    OF    THEIR 

SURFACE 188 

1.  EARTH  ROADS 189 

How  to  improve  them ib. 

Effects  of  wheels  on  their  surface 191 

2.  GRAVELROADS 193 

Directions  for  their  construction ib 


10  CONTENTS. 

PAOI 

3.  BROKEN-STONE  ROADS 194 

McAdara  roads ib. 

Fundamental  principles 195 

Quality  of  the  stone 196 

Size  of  the  broken  stones 198 

Breaking  them 199 

Thickness  of  the  coating 900 

Application  of  the  materials 201 

Rolling  thenewroad 204 

Keeping  tip  the  road 205 

Repairing  it. 209 

Tolford  roads 210 

Specification ib. 

Propriety  of  a  pavement  foundation 212 

Foundation  of  concrete 215 


4*   PAVED  ROADS 216 

Pebble  pavements .. ib 

Squared  stone  pavements 217 

Foundations 218 

Of  sand. ib. 

Of  broken  stones 219 

Ofpebbles ib. 

Ofconcrete ii 

Quality  of  stone 220 

Sizeand  shape 221 

Arrangement 222 

Manner  of  laying 223 

Borders  and  curbs 224 

Advantages 225 

Paved  and  McAdam  roads  compared. ib. 

Roman  roads 226 

6.  KOADS  OF  WOOD 228 

Logs ib, 

Charcoal 229 

Plank . 330 

Blocks ;, 364 


CONTENTS.  11 

PAGB 

6.  ROADS  OF  OTHER  MATERIALS. 255 

Bricks ib. 

Concrete ib. 

Cast  iron ib. 

Asphaltum 256 

Caoutchouc ib. 

7.  ROADS  WITH  TRACKWAYS : 257 

Of  stone ib. 

Of  wood. 259 

Of  iron....                                                                   ...  260 


CHAPTER  V.— RAIL-ROADS. 261 

I.  WHAT  RAIL-ROADS  OUGHT  TO  BE 264 

1.  AS  TO  THEIR  DIRECTION 270 

Economy  of  straightness~ ib. 

Evils  of  curves 271 

2.  AS  TO  THEIR  GRADES 276 

Loss  of  power  on  ascents. ib. 

Compensating  power  of  descents 280 

3.  AS  TO  THEIR  CROSS-SECTION 282 

The  broad  and  narrow  gauge  question ib. 

Advantages  of  the  broad  gauge 283 

Objections  to  it 284 

The  break  of  gauge 285 

Width  of  road-bed....,  ...288 


II.  THE  LOCATION  OF  RAIL-ROADS 290 

III    THE  CONSTRUCTION  OF  RAIL-ROADS 291 

1.  FORMDtfG  THE  ROAD-BED * a. 

Excavations. »&. 

Tunnels 293 

Embankments 294 

Ballasting 296 


12  CONTENTS. 

PAOi 

2.  THE  SUPERSTRUCTURE 297 

Rails  supported  at  intervals ib. 

Their  shape- ib. 

Theirwelgbt rt. 

The  distances  of  their  supports ii 

Their  end  joints. 300 

Theirohairs 301 

Stone  blocks 303 

Wooden  cross-sleepers 304 

Bails  on  continuous  supports. 305 

Inclination  of  the  rails 308 

Elevation  of  the  outer  raiL t'6 

Sidings,  crossings,  «fcc- 809 

Single  rail  railroad. 311 

IV.  THE  MOTIVE  POWERS  OF  RAIL-ROADS 312 

1.  HORSEPOWER. ib. 

Table  of  power  at  different  speeds. ib. 

2.  STATIONARY  ENGINES 313 

A  Broadway  railroad. 814 

3.  LOCOMOTIVE  ENGINES 318 

History t'6. 

Principles 321 

Speed  and  power 324 

Working  expenses 826 

Safety  of  travelling 328 

Signals 381 

%.  ATMOSPHERIC  PRESSURE 334 

History  of  its  application. t'6. 

Description  of  present  system, 885 

Advantages. 836 


CONTENTS.  13 


CHAPTER     VI.— THE     MANAGEMENT     OF 

TOWN   ROADS 341 

The  present  Road- tax  system 342 

Its  defects 343 

New  system  proposed 345 

APPENDIX  A. 

CALCULATIONS  OF  EXCAVATION  AND  EMBANKMENT 349 

By  averaging  end  areas  S5S 

Error  in  excess 355 

By  the  middle  areas 856 

Error  in  defect 337 

By  the  Prismoidal  formula ib. 

Proof  of  its  correctness ..  359 

Easier  rules 360 

Formula  for  a  series  of  equal  distance 362 

By  mean  proport  ionals 365 

When  the  ground  is  sidelong.. 365 

When  the  surface  is  warped 367 

Three  level  ground 383 

Irregular  ground 387 

On  curves 388 

Explanation  of  tables 389 

APPENDIX  B.     Location  of  roads 390 

"          C.     Rail-road  curves 396 

"          D.     Estimation 420 

"          E.     Tunnels 424 

F.     Bridges 437 

"          G.     Specifications 449 

Rail-road  resistances 453 

Stoking  out  side-slopes 4S7 

Tables  for  calculating  earthwork 460 


A 

MANUAL  OF  ROAD-MAKING. 


INTRODUCTION.^ 

THE  ROADS  of  a  country  are  accurate  and  certain  tests 
of  the  degree  of  its  civilization.  Their  construction  is 
one  of  the  first  indications  of  the  emergence  of  a  people 
from  the  savage  state  ;  and  their  improvement  keeps  pace 
with  the  advances  of  the  nation  in  numbers,  wealth,  in- 
dustry, and  science — of  all  which  it  is  at  once  an  element 
and  an  evidence. 

Roads  are  the  veins  and  arteries  of  the  body  politic, 
for  through  them  flow  the  agricultural  productions  and  the 
commercial  supplies  which  are  the  life-blood  of  the  state. 
Upon  the  sufficiency  of  their  number,  the  propriety  of 
their  directions,  and  the  unobstructedness  of  their  courses,  . 
depend  the  ease  and  the  rapidity  with  which  the  more 
distant  portions  of  the  system  receive  the  nutriment  which 
is  essential  to  their  life,  health,  and  vigor,  and  without  a 
copious  supply  of  which  the  extremities  must  languish 
and  die. 

But  roads  belong  to  that  unappreciated  class  of  bless 
ings,  of  which  the  value  and  importance  are  not  fully  felt 
because  of  the  very  greatness  of  their  advantages,  which 
are  so  manifold  and  indispensable,  as  to  have  rendered 
their  extent  almost  universal  and  their  origin  forgotten. 
Perhaps  we  will  better  appreciate  them,  if  we  endeavor  to 


16  A    MANUAL    OF   ROAD-MAKING. 

imagine  what  would  be  our  condition  if  none  had  ever 
been  constructed. 

Suppose,  then,  that  a  traveller  had  occasion  to  go  from 
Boston  to  Albany,  and  that  no  road  between  the  two 
places  was  yet  in  existence.  In  the  first  place,  how  would 
he  find  his  way  ?  Even  if  he  knew  that  his  general  di- 
rection should  be  towards  the  setting  sun,  thq  sun  would 
be  often  hidden  by  day,  and  the  stars  by  night ;  and,  there 
being  no  roads,  there  would  be  no  engineers  and  no  sur- 
veyor's compass.  The  moss  upon  tjie  north  side  of  the 
trees  might  be  in  some  degree  a  guide  to  him,  if  he  were 
skilled  in  woodcraft ;  but  he  would  at  last  become  so  be- 
wildered, that,  like  lost  hunters  on  the  prairies,  he  would 
begin  to  believe  that  the  sun  rose  in  the  west,  set  in  the 
east,  and  was  due  north  at  mid-day. 

Allowing,  however,  that  he  was  fortunate  enough  to 
retain  the  true  direction,  would  he  be  able  to  follow  it ? 
In  the  forest  he  must  force  for  himself  a  passage  through 
the  tangled  underwood,  and  make  long  circuits  around  the 
fallen  trees,  which  no  axe-men  have  as  yet  cleared  away. 
Through  the  swamp  he  must  struggle  amid  the  slippery 
«nd  deceitful  mud,  for  no  road-maker  has  yet  built  the 
causeway.  Over  the  mountain  he  must  clamber  only  to 
again  descend,  for  topographical  science  has  not  taught 
him  how  much  he  would  gain  by  winding  around  its  base. 
The  rocky  walls  of  precipices  he  must  arduously  climb, 
and  perilously  descend,  for  no  engineer  has  as  yet  blasted 
a  passage  through  them.  Meeting  a  deep  river,  or  even 
a  mere  mountain  torrent,  if  he  cannot  ford  or  swim  it,  he 
must  seek  its  head  with  many  miles  of  added  travel,  to  be 
doubled  again  by  his  return  to  his  original  direction.  All 
this  while,  too,  he  can  subsist  only  by  precarious  hunting ; 
for,  there  being  no  roads,  there  would  be  no  inns,  and 


INTRODUCTION.  17 

he  can  scaicely  carry  himself  along,  much  less  a  store  of 
provisions. 

Look  now  at  the  contrast,  and  at  the  ease,  speed,  and 
comfort  with  which  the  modern  traveller  flies  from  place 
to  place  upon  that  best  of  all  roads,  a  railroad. 

But  the  increase  of  personal  comfort  is  only  a  petty 
item  in  estimating  the  importance  of  roads,  even  in  despite 
of  Dr.  Johnson's  exclamation,  that  life  has  no  greater 
pleasure  than  being  whirled  over  a  good  road  in  a  post- 
chaise.  More  important  is  the  consideration,  that,  in 
the  absence  of  such  facilities,  the  richest  productions 
of  nature  waste  on  the  spot  of  their  growth.  The  lux- 
uriant crops  of  our  western  prairies  are  sometimes  left 
to  decay  on  the  ground,  because  there  are  no  rapid  and 
easy  means  of  conveying  them  to  a  market.  The  rich 
mines  in  the  northern  part  of  the  state  of  New  York  are 
comparatively  valueless,  because  the  roads  among  the 
mountains  are  so  few  and  so  bad,  that  the  expense  of  the 
transportation  of  the  metal  would  exceed  its  value.  So, 
too,  in  Spain,  it  has  been  known  after  a  succession  of 
abundant  harvests,  that  the  wheat  has  actually  been  al- 
lowed to  rot,  because  it  would  not  repay  the  cost  of  car- 
riage.* In  that  country,  for  similar  reasons,  sheep  are 
killed  for  their  fleece  only,  and  the  flesh  is  abandoned  ;  as 
is  likewise  the  case  with  cattle  in  Brazil,  slaughtered 
merely  for  their  hides. 

Such  are  the  effects  of  the  almost  total  want  of  roads. 
Among  those  which  do  exist,  the  difference,  as  to  ease, 
rapidity,  and  economy  of  transportation,  caused  by  the  va- 
rious degrees  of  skill  and  labor  bestowed  upon  them,  is 
much  greater  than  is  usually  imagined,  particularly  by 
farmers,  whom  they  most  concern. 

*  Edinburgh  Review,  Ixv.  448. 
2 


18  A    MANUAL    OF    ROAD-MAKING 

One  important  difference  lies  in  the  grades  or  longitu- 
dinal slopes  of  a  road.  Suppose  that  a  road  rises  a  hun- 
dred feet  in  the  distance  of  two  thousand  feet.  Its  ascend- 
ing slope  is  then  one  in  twenty,  and  (as  will  be  hereafter 
proven)  one-twentieth  of  the  whole  load  drawn  over  it  in 
one  direction,  must  be  actually  lifted  up  this  entire  height 
of  one  hundred  feet.  But  upon  such  a  slope  a  horse  can 
draw  only  one  half  as  much  as  he  can  upon  a  level  road, 
and  two  horses  will  be  needed  on  such  a  road  to  do  the 
usual  work  of  one.  If  the  road  be  intrusted  to  the  care 
of  a  skilful  engineer,  and  be  made  level  by  going  round 
hills  instead  of  over  them,  or  in  any  other  way,  there  will 
be  a  saving  of  one  half  of  the  former  expense  of  carriage 
on  it. 

Another  great  difference  in  roads  lies  in  the  nature  of 
their  surfaces ;  one  being  hard  and  smooth,  and  another 
soft  and  uneven.  On  a  well-made  road  of  broken  stone,  a 
horse  can  draw  three  times  as  much  as  he  can  upon  a 
gravel  road.  By  making,  then,  such  a  road  as  the  former 
(according  to  the  instructions  in  Chapter  IV.)  in  the  place 
of  the  latter,  the  expenses  of  transportation  will  be  re- 
duced to  one-third  of  their  former  amount,  so  that  two- 
thirds  will  be  completely  saved,  and  two  out  of  three  of  all 
the  horses  formerly  employed  can  then  be  dispensed  with.* 
If  such  an  improvement  can  be  made  for  a  sum  of  money, 
the  interest  of  which  will  be  less  than  the  total  amount  of 
the  annual  saving  of  labor,  it  will  be  true  economy  to 
make  it,  however  great  the  original  outlay ;  for  the  de 

•  In  the  absence  of  such  an  improvement,  when  the  Spanish  govern- 
ment required  a  supply  of  grain  to  be  transferred  from  Old  Castile  to 
Madrid,  30,000  horses  and  mules  were  necessary  for  the  transportation  of 
480  tons  of  wheat  Upon  a  broken-stone  road  of  the  best  sort,  onc-hun 
diedth  of  that  number  could  easily  have  done  the  work. 


INTRODUCTION.  19 

cision  of  all  such  questions  depends  on  considerations  of 
comparative  profit.  This  part  of  the  subject  will  be  more 
minutely  examined  at  the  end  of  Chapter  I.,  in  considering 
"  What  roads  ought  to  be  as  to  their  cost." 

The  profits  of  such  improvements  are  not  confined  to  the 
proprietors  of  a  road,  (whether  towns,  or  companies  re 
munerated  for  these  expenditures  by  tolls)  but  are  shared 
by  all  who  avail  themselves  of  the  increased  facilities  ; 
consumers  and  producers,  as  well  as  road-owners.  If 
wheat  be  worth  in  a  city  a  dollar  per  bushel,  and  if  it 
cost  25  cents  to  transport  it  thither  from  a  certain  farming 
district,  it  will  there  necessarily  command  only  75  cents. 
If  now  by  improved  roads  the  cost  of  carriage  is  reduced 
to  10  cents,  the  surplus  15  cents  on  each  bushel  is  so  much 
absolute  gain  to  the  community,  balanced  only  by  the  cost 
of  improving  the  road.  Supposing  that  a  toll  of  5  cents 
will  pay  a  fair  dividend  on  this,  there  remains  10  cents  per 
bushel  to  be  divided  between  the  producer  and  the  con 
sumer,  enabling  the  former  to  sell  his  wheat  at  a  higher 
price  than  before,  while  at  the  same  time  the  latter  obtains 
it  at  a  less  cost. 

Agriculture  is  thus  directly,  and  likewise  indirectly,  de 
pendent  in  a  great  degree  upon  good  roads  for  its  success 
and  rewards.  Directly,  as  we  have  just  seen,  these  roads 
carry  the  productions  of  the  fields  to  the  markets,  and 
bring  to  them  in  return  their  bulky  and  weighty  materials 
of  fertilization,  at  a  cost  of  labor  which  grows  less  and  less 
as  the  roads  become  better.  Indirectly,  the  cities  and 
towns,  whose  dense  population  and  manufacturing  indus- 
try make  them  the  best  markets  for  fanning  produce, 
are  enabled  to  grow  and  to  extend  themselves  indefinitely 
by  roads  alone,  which  supply  the  place  of  rivers,  to  the 
banks  of  which  these  great  towns  would  otherwise  be  ne- 


20  A    MANUAL    OI     ROAD-MAKING. 

cessarily  confined.*  While,  therefore,  it  would  be  an  in- 
excusable waste  of  money  to  construct  a  costly  road  to 
connect  two  small  towns  which  had  little  intercourse,  it 
would  be  equally  wasteful,  and  is  a  much  more  frequent 
short-sightedness  of  economy,  to  leave  unimproved  and 
almost  in  a  state  of  nature,  the  communications  between 
a  great  city  and  the  interior  regions  from  which  its  daily 
sustenance  is  drawn,  and  into  which  its  own  manufactures 
are  conveyed. 

Some  of  the  advantages  thus  to  be  attained,  have  been 
well  summed  up  in  a  report  of  a  committee  of  the  House 
of  Commons  : 

"  By  the  improvement  of  our  roads,  every  branch  oi 
our  agricultural,  commercial,  and  manufacturing  industry 
would  be  materially  benefited.  Every  article  bi  ought  to 
market  would  be  diminished  in  price  ;  and  the  r  umber  of 
horses  would  be  so  much  reduced  that,  by  these  and  other 
retrenchments,  the  expense  of  FIVE  MILLIONS  [pounds 
sterling]  would  be  ANNUALLY  saved  to  the  public.  The 
expense  of  repairing  roads,  and  the  wear  and  tear  of  car- 
riages and  horses,  would  be  essentially  diminished  ;  and 
thousands  of  acres,  the  produce  of  which  is  now  wasted 
in  feeding  unnecessary  horses,  would  be  devoted  to  the 
production  of  food  for  man.  In  short,  the  public  and 
private  advantages  which  would  result  from  effecting  that 
great  object,  the  improvement  of  our  highways  and  turn- 
pike roads,  are  incalculable  ;  though,  from  their  being 
spread  over  a  wide  surface,  and  available  in  various  ways, 
such  advantages  will  not  be  so  apparent  as  those  derived 
from  other  sources  of  improvement,  of  a  more  restricted 
and  less  general  nature." 

*  McCulloch,  Dictionary  of  Commerce. 


IIS  PRODUCTION.  21 

The  changes  in  the  condition  of  a  country  which  such 
improvements  effect,  are  of  the  highest  importance.  There 
is  as  much  truth  as  blundering  in  the  famous  couplet  win- 
ten  by  an  enthusiastic  admirer  of  the  roads  which  Marsha] 
Wade  opened  through  the  Scottish  Highlands  : 

"  Oh,  had  you  only  seen  these  roads  before  they  were  made, 
You  would  lift  up  your  eyes  and  bless  Marshal  Wade  !" 

His  military  road  is  said  to  have  done  more  for  the  civih 
zation  of  the  Highlands  than  the  preceding  efforts  of  all 
the  British  monarchs.  But  the  later  roads  under  the  more 
scientific  direction  of  Telford,  produced  a  change  in  the 
state  of  the  people  which  is  probably  unparalleled  in  the 
history  of  any  country  for  the  same  space  of  time.  Large 
crops  of  wheat  now  cover  former  wastes  ;  farmers,  houses 
and  herds  of  cattle  are  now  seen  where  was  previously  a 
desert ;  estates  have  increased  sevenfold  in  value  and 
annual  returns  ;  and  the  country  has  been  advanced  al 
least  one  hundred  years.  In  Ireland  similar  effects  have 
been  produced,  and  the  face  of  the  country  in  some  dis- 
tricts has  been  completely  renovated.  The  enlarged  labors 
of  the  public  works,  now  undertaken  in  that  country  by 
the  government,  though  commenced  only  for  temporary 
relief,  will  not  fail  to  produce  great  permanent  benefits. 

The  moral  results  of  such  improvements  are  equally 
admirable.  Telford  testifies  that  in  the  Highlands  they 
greatly  changed  for  the  better  the  habits  of  the  great 
working  class.  Thus,  too,  when  Oberlin  wished  to  im- 
prove the  spiritual  condition  of  his  rude  flock,  he  began 
by  bettering  their  physical  state,  and  led  out  his  whole 
people  to  open  a  road  of  communication  between  theii 
secluded  valley  and  the  great  world  without.  The  won- 
derful moral  and  intellectual  amelioration  which  ensued 


22  A    MANUAL    OF    ROAD-MAKING. 

was  an  unmistakeable  tribute  to  the  civilizing  and  eleva 
ling  influence  of  good  roads. 

Among  the  most  remarkable  consequences  of  the  im- 
provement of  roads,  is  the  rapidly  increasing  proportion  in 
which  their  benefits  extend  and  radiate  in  every  direction, 
as  impartially  and  benignantly  as  the  similarly  diverging 
rays  of  the*  sun.  Around  every  town  or  market-place  we 
may  conceive  a  number  of  concentric  circles  to  be  drawn, 
enclosing  areas  from  any  part  of  which  certain  kinds  of 
produce  may  be  profitably  taken  to  the  town ;  while  from 
any  point  beyond  each  circumference,  the  expense  of  the 
carriage  of  the  particular  article  would  exceed  its  value. 
Thus  the  inner  circle,  at  the  centre  of  which  is  the  town, 
may  show  the  limit  in  every  direction  from  beyond  which 
perishable  vegetables,  or  articles  very  bulky  or  heavy  in 
proportion  to  their  value,  cannot  be  profitably  brought  to 
market ;  the  next  larger  circle  may  show  the  limit  of 
fruits  ;  and  so  on.  If  now  the  roads  are  improved  in  any 
way,  so  as  in  any  degree  to  lessen  the  expense  of  car- 
riage, the  radius  of  each  circle  is  correspondingly  in- 
creased, and  the  area  of  each  is  enlarged  as  the  square  of 
this  ratio  of  increase.  Thus,  if  the  improvement  enables 
a  horse  to  draw  twice  as  much  or  to  travel  twice  as  fast 
as  he  did  before,  each  of  the  limiting  circles  is  expanded 
outward  to  twice  its  former  radius,  and  embraces  foui 
times  -its  former  area.  If  the  rate  of  improvement  be 
threefold,  the  increase  of  area  is  ninefold  ;  and  so  on 
All  the  produce,  industry,  and  wealth,  which  by  these  im 
provements  finds,  for  the  first  time,  a  market,  is  as  it  were 
a  new  creation.* 

The  number  of  passengers  is  governed  by  similar  laws ; 

•  Dr.  Anderson. 


INTRODUCTION.  23 

and  the  increased  facilities  of  a  better  road  attract  them 
from  inferior  ones,  as  the  digging  of  a  new  and  deep  well 
often  drains  the  water  from  all  the  shallow  ones  in  its 
neighborhood.  _The  distance  to  the  right  and  left  of  the 
new  road,  from  which  it  will  attract  passengers,  admits  of 
a  mathematical  investigation,  which  will  be  found  at  the 
end  of  Chapter  I. ;  and  the  deductions  of  theory  are  amply 
corroborated  by  the  observations  of  experience,  and  more 
than  realized  in  the  improvement  of  every  old  road  and  the 
opening  of  every  new  one  ;  for  not  only  is  the  former 
travel  attracted  from  great  distances  in  every  direction, 
but  a  very  considerable  amount  is  created. 

Supposing  that  by  these  improvements  the  average 
speed  over  a  whole  country  be  only  doubled,  the  whole 
population  of  the  country  (to  borrow  a  metaphor  from  an 
accomplished  writer)  would  have  advanced  in  mass,  and 
placed  their  chairs  twice  as  near  to  the  fireside  of  their 
metropolis,  and  twice  as  near  to  each  other.  If  the  speed 
were  again  doubled,  the  process  would  be  repeated;  and  so 
on.  As  distances  were  thus  gradually  annihilated,  the  whole 
surface  of  the  country  would  be,  as  it  were,  contracted  and 
condensed,  till  it  was  only  one  immense  city ;  and  yet, 
by  one  of  the  modern  miracles  of  science  wedded  to  art, 
every  man's  field  would  be  found  not  only  where  it  always 
was,  but  as  large  as  ever  it  was,  and  even  far  larger,  esti- 
mating its  size  by  the  increased  profits  of  its  productions. 
The  more  perfect  the  roads,  the  more  rapidly  would  this 
result  be  attained,  and  therefore  most  quickly  of  all  by 
railroads. 

But  howevei  great  the  advantages  of  railroads,  as  to 
mere  speed,  and  however  precious  to  the  hurrying  travel- 
ler their  triumphs  over  time  and  space,  COMMON  ROADS  will 
always  be  incomparably  more  valuable  to  the  community 


,34  A    MANUAL    O      JROAU-MAKiNG. 

at  large.  The  distinguishing  characteristic  of  a  modern  rail 
road,  as  compared  with  a  "  tram  road,"  and  that  to  which 
its  peculiar  power  is  chiefly  due,  is  the  projecting  flanges- 
of  the  wheels  of  its  carriages,  by  which  they  are  retained 
upon  the  rails.  But  this  peculiarity,  in  an  equal  degree, 
lessens  its  advantages  to  the  agricultural  population  ;  since 
the  vehicles  which  are  adapted  to  travel  on  railroads  can 
not  be  used  on  the  common  roads  leading  to  them,  nor  in 
the  ordinary  labors  of  the  farm  ;  while  on  all  other  im 
proved  roads  the  same  wagons,  horses,  and  men,  employed 
at  one  season  in  cultivating  the  ground,  can  also  be  pro- 
fitably employed,  in  their  otherwise  idle  moments,  in  con- 
veying the  produce  to  a  market.  For  these  reasons,  even  if  a 
railroad  came  to  every  man's  door,  he  could  more  economi 
cally  use  a  good  common  road  ;  but  since,  on  the  con- 
trary, the  expense  of  the  construction  of  railroads  must  al 
ways  restrict  them  to  important  lines  of  communication, 
(where,  indeed,  their  value  can  scarcely  be  estimated  loo 
highly)  in  every  other  situation,  the  greatest  good  of  the 
greatest  number,  and  the  most  universal  benefits  with  the 
fewest  accompanying  evils,  will  be  most  effectually  se- 
cured, by  improving  (in  accordance  with  the  principles 
to  be  presently  set  forth)  the  peoples  highways — the 
common  roads  of  the  country. 

In  this  analytical  examination  of  the  subject  of  ROAD- 
MAKING,  it  will  be  considered  under  the  following  general 
heads : 

1 .  What  Roads  ought  to  be. 

2.  Their  Location. 

3.  Their  Construction. 

4.  Improvement  of  their  Surface 


CHAPTER  I. 

WHAT    ROADS    OUGHT    TO    BE. 

*  The  art  of  Road-making  must  essentially  depend  for  its  success  on 
its  being  exercised  in  conformity  with  certain  general  principles ;  and 
their  justness  should  be  rendered  so  clear  and  self-evident  as  not  to  admit 
of  any  controversy." 

SIR  HENRY  PARNELL. 

RAPIDITY,  safety,  and  economy  of  carriage  are  the  ob- 
jects of  roads.  They  should  therefore  be  so  located  and 
constructed  as  to  enable  burdens,  of  goods  and  of  passen- 
gers, to  be  transported  from  one  place  to  another,  in  the 
least  possible  time,  with  the  least  possible  labor,  and,  con- 
sequently, with  the  least  possible  expense. 

To  attain  these  important  ends,  a  road  should  fulfil  cer- 
tain conditions,  which  the  nature  of  the  country  over  which 
it  passes,  and  other  circumstances,  may  render  impossible 
to  unite  and  reconcile  in  one  combination;  but  to  the  union 
of  which  we  should  endeavor  to  approximate  as  nearly  as 
possible  in  forming  an  actual  road  upon  the  model  of  this 
ideally  perfect  one.  We  will  therefore  investigate — 

WHAT  ROADS  OUGHT  TO  BE, 

1.  As  to  their  direction. 

2.  As  to  their  slopes. 

3.  As  to  their  cross-section 

4.  As  to  their  surface. 

5.  As  to  their  cost. 


26  WHAT    ROADS    OUGHT    TO    BE. 

1.  WHAT  ROADS  OUGHT  TO  BE,  AS  TO  THEIR  DIRECTION. 
IMPORTANCE    OF    STRAIGHTNESS. 

Every  road,  other  things  being  equal,  should  be  per- 
fectly straight,  so  that  its  length,  and,  therefore,  the  lime 
and  labor  expended  in  travelling  upon  it,  should  be  the  least 
possible  ;  i.  e.,  its  alignemens,  or  directions,  departing 
from  one  extremity  of  it,  should  constantly  tend  towards 
the  other 

Any  unnecessary  excess  of  length  causes  a  constant 
threefold  waste  ;  firstly,  of  the  interest  of  the  capital  ex- 
pended in  making  that  unnecessary  portion  ;  secondly,  of 
the  ever-recurring  expense  of  repairing  it ;  and,  thirdly,  of 
the  time  and  labor  employed  in  travelling  over  it.  It  will 
therefore  be  good  economy  to  expend,  in  making  topo- 
graphical examinations  for  the  purpose  of  shortening  the 
road,  any  amount  less  than  not  only  that  sum  which  the 
distance  thus  saved  would  have  cost,  but,  in  addition,  that 
principal  which  corresponds  to  the  annual  cost  of  the  re- 
pairs and  of  the  labor  of  draught  which  would  have  been 
wasted  upon  this  unnecessary  length. 

ADVANTAGES    OF    CURVING. 

The  importance  of  making  the  road  as  level  as  possible 
will  be  explained  in  the  next  section,  and  as  a  road  can  in 
few  cases  be  at  the  same  time  straight  and  level,  these  two 
requirements  will  often  conflict.  In  such  cases,  straightness 
should  always  be  sacrificed  to  obtain  a  level,  or  to  make 
the  road  less  steep.  This  is  one  of  the  most  important 
principles  to  be  observed  m  laying  out  or  improving  a  road, 
and  it  is  the  one  most  often  violated. 

A  straight  road  over  an  uneven  and  hilly  counlry  may, 
at  first  view,  when  merely  seen  upon  the  map,  be  pro 


.ADVANTAGES    OF    CURVING.  27 

nounced  to  be  a  bad  road  ;  for  the  straightness  musi  have 
been  obtained  either  by  submitting  to  steep  slopes  in  as- 
cending the  hills  and  descending  into  the  valleys,  or  these 
natural  obstacles  must  have  been  overcome  by  incurring 
a  great  and  unnecessary  expense  in  making  deep  cuttings 
and  fillings. 

A  good  road  should  wind  around  these  hills  instead  of 
running  over  them,  and  this  it  may  often  do  without  atal! 
increasing  its  length.  For  if  a  hemisphere  (such  as  half 
a  bullet)  be  placed  so  as  to  rest  upon  its  plane  base,  the 
halves  of  great  circles  which  join  two  opposite  points  of 
this  base  are  all  equal,  whether  they  pass  horizontally  or 
vertically.  Or  let  an  egg  be  laid  upon  a  table,  and  it  will 
be  seen  that  if  a  level  line  be  traced  upon  it  from  one  end 
to  the  other,  it  will  be  no  longer  than  the  line  traced  be- 
tween the  same  points,  but  passing  over  the  top.  Pre- 
cisely so  may  the  curving  road  around  a  hill  be  often  no 
longer  than  the  straight  one  over  it ;  for  the  latter  road  is 
straight  only  with  reference  to  the  vertical  plane  which 
passes  through  it,  and  is  curved  with  reference  to  a  hori- 
zontal plane  ;  while  the  former  level  road,  though  curved 
as  to  the  vertical  plane,  is  straight  as  to  a  horizontal  one. 
Both  lines  thus  curve,  and  we  call  the  latter  one  straight 
in  preference,  only  because  its  vertical  curvature  is  less 
apparent  to  our  eyes. 

The  difference  in  length  between  a  straight  road  and 
one  which  is  slightly  curved  is  very  small.  If  a  road  be- 
tween two  places  ten  miles  apart  were  made  to  curve  so 
that  the  eye  could  nowhere  see  farther  than  a  quarter  of 
a  mile  of  it  at  once,  its  length  would  exceed  that  of  a 
perfectly  straight  road  between  the  same  points  by  only 
about  one  hundred  and  fifty  yards.* 

*  Sganzin,  p.  89. 


28  WHAT    ROADS    OUGHT   TO    BE. 

But  even  if  the  level  and  curved  road  were  very  much 
longer  than  the  straight  and  steep  one,  it  would  almost 
always  be  better  to  adopt  the  former ;  for  on  it  a  horse  could 
pafely  and  rapidly  draw  his  full  load,  while  on  the  other  he 
could  carry  only  part  of  his  load  up  the  hill,  and  must  di- 
minish his  speed  in  descending  it.  As  a  general  rule,  the 
horizontal  length  of  a  road  may  be  advantageously  in- 
creased, to  avoid  an  ascent,  by  at  least  twenty  times  the 
perpendicular  height  which  is  to  be  thus  saved  ;  that  is,  to 
escape  a  hill  a  hundred  feet  high,  it  would  be  proper  for 
the  road  to  make  such  a  circuit  as  would  increase  its 
length  two  thousand  feet.*  The  mathematical  axiom  that 
"  a  straight  line  is  the  shortest  distance  between  two 
points,"  is  thus  seen  to  be  an  unsafe  guide  in  road- 
imking,  and  less  appropriate  than  the  paradoxical  proverb 
that  "  the  longest  way  around  is  the  shortest  way  home.' 

The  gently  curving  road,  besides  its  substantial  advan 
tages,  is  also  much  more  pleasant  to  the  traveller  upon  it ; 
for  he  is  not  fatigued  by  the  tedious  prospect  of  a  long 
straight  stretch  of  road  to  be  traversed,  and  is  met  at  each 
curve  by  a  constantly  varied  view. 

It  cannot  oe  too  strongly  impressed  upon  a  road-maker, 
that  straighlness  is  not  the  highest  characteristic  of  a  good 
road.  As  says  Coleridge — 

"  Straight  forward  goes 

The  lightning's  flash,  and  straight  the  fearful  path 
Of  the  cannon-ball." 

But  in  striking  contrast  he  adds — 

"  The  ROAD  the  human  being  travels, 
That  on  which  blessing  comes  and  goes,  doth  follow 
The  river's  course,  the  valley's  playful  windings, 
Curves  round  the  cornfield  and  the  hill  of  vines."t 

*  This  proportion  depends  on  the  degree  of  friction  assumed,  c  eubject 
U-  be  investigated  in  a  following  section, 
f  The  Viccolomini.  i.  4 


DISADVANTAGES    OF    STRAIGHTNESS.  29 

The  passion  for  straightness  is  the  great  fault  in  the 
location  of  most  roads  in  this  country,  which  too  often 
remind  us  how 

"  The  king  of  France,  with  forty  thousand  men, 
Marched  up  a  hill,  and  then — marched  down  again  ;" 

so  generally  do  they  clamber  over  hills  which  they  could 
so  much  more  easily  have  gone  around  ;  as  if  their  ma- 
kers, like  Marshal  Wade,  had  "  formed  the  heroic  deter- 
mination of  pursuing  straight  lines,  and  of  defying  nature 
and  wheel-carriages  both,  at  one  valiant  effort  of  courage 
and  of  science." 

One  reason  of  this  is,  that  the  houses  of  the  first  set- 
tlers were  usually  placed  on  hill-tops,  (to  escape  the  poi- 
sonous miasmata  of  the  undrained  swamps,  and  to  detect 
the  approach  of  the  hostile  savages)  and  that  the  first 
roads  necessarily  ran  from  house  to  house.  Our  error 
consists  in  continuing  to  follow  these  primitive  roads  with 
our  great  thoroughfares.  These  original  paths  were  also 
traversed  only  by  men,  and  therefore  very  properly  fol- 
lowed the  shortest  though  steepest  route.  Tracks  for 
pack-horses  came  next,  and  a  considerable  degree  of 
steepness  is  admissible  in  them  also.  Wheeled  carriages 
were  finally  introduced  and  brought  into  use  upon  the 
same  tracks,  though  too  steep  for  true  economy  of  labor 
with  them — the  standard  of  slope  being  very  different  for 
foot,  horse,  and  carriage  roads  Before  sufficient  attention 
was  paid  to  the  subject,  the  lands  on  either  side  of  the 
road  had  been  fenced  off  and  appropriated  by  individuals, 
and  thu?  the  random  tracks  became  the  ]cgal  highways. 

The  evil  is  now  perpetuated  by  the  m.  willingness  of 
farmers  to  allow  a  road  to  run  through  thek  farms  in  a 
winding  line.  The)  attach  more  importance  K  the  square 


30 


WHAT    ROADS    OUGHT    TO    BE. 


ness  of  their  fields  than  to  the  improvement  of  the  lines 
of  their  roads — not  being  aware  how  much  more  labor  is 
wasted  by  them  in  travelling  over  these  steep  roads,  than 
there  would  be  in  cultivating  an  awkward  corner  of  a 
field. 

This  feeling  is  seen  carried  to  excess  in  some  of  the 
now  states  of  the  West,  in  which  the  roads  now  run  along 
"  section-lines,"  and  as  these  sections  are  all  squares,  with 
sides  directed  towards  the  cardinal  points  of  the  compass, 
a  person  wishing  to  cross  the  country  in  any  other  direc- 
tion than  North,  South,  East  or  West,  must  do  so  in  rec- 
tangular zigzags. 

PLEASURE    DRIVES. 

In  reads  designed  solely  for  pleasure  drives,  such  as 
those  laid  out  by  landscape  gardeners  in  parks,  cemeteries, 
&c.,  curvature  is  the  rule,  and  straightness  only  the  ex- 
ception. In  them  the  object  is  to  wind  as  much  as  possible, 
in  Hogarth's  "  line  of  grace,"  so  as  to  obtain  the  greatest 
development  of  length  which  the  area  of  the  ground  will 
permit,  but  at  the  same  time  never  to  appear  to  turn  for 
llie  mere  sake  of  curving.  Some  reason  for  the  windings 
must  always  be  suggested,  such  as  a  clump  of  trees,  a  rise 
of  ground,  a  good  point  of  view,  or  any  object  which  may 
conceal  the  artifice  employed.  The  visitor  must  be  de- 
ceived into  the  belief  that  he  is  travelling  over  a  large  area, 
while  he  is  truly  only  retracing  his  steps  and  constantly 
doubling  upon  his  track  ;  but  he  must  do  it  unconsciously, 
or  at  least  without  knowing  the  precise  manner  in  which 
the  pleasant  deception  is  effected.  Arx  est  celare  artem. 

The  map  on  the  opposite  page,  representing  the  roads 
and  paths  in  Greenwood  Cemetery,  will  somewhat  illus- 
trate this  principle 


ROAtS    IN    GREENWOOD    CEMETERY.  31 


WHAT    ROADS    OUGHT    TO    BE. 


2.    WHAT  ROADS  OUGHT  M  O  BE  AS  TO  THEffi  SLOPES. 


LOSS    OF    POWER    ON    INCLINATIONS. 

Every  road  should  be  perfectly  level.  If  it  be  not,  a 
large  portion  of  the  strength  of  the  horses  which  travel  it 
will  be  expended  in  raising  the  load  up  the  ascent.  When 
a  weight  is  drawn  up  an  inclined  plane,  the  resistance  of 
the  force  of  gravity,  or  the  weight  to  be  overcome,  is  such 
a  part  of  the  whole  weight,  as  the  height  of  the  plane  is  oi 
its  length  If,  then,  a  road  rises  one  foot  in  every  twenty 
of  its  length,  a  horse  drawing  up  it  a  load  of  one  ton  is 
compelled  to  actually  lift  up  one-twentieth  of  the  whole 
weight,  i.  e.,  one  hundred  pounds,  through  the  whole 
height  of  the  ascent,  besides  overcoming  the  friction  of 
the  entire  load. 

Fig.  2. 

Let  DE  re- 
present the  in- 
clined surface 
of  a  road  upon 
which  rests  a 
wagon,  the  cen- 
tre of  gravity  of 
which  is  sup- 
posed to  be  at 

C.  Draw  CA  perpendicular  to  the  horizon,  and  CB  perpen- 
dicular to  the  surface  of  the  hill.  Let  CA  represent  the  force 
of  gravity,  or  the  weight  of  the  wagon  and  its  load.  It  is 
equivalent,  in  magnitude  and  direction,  to  its  two  rectangular 
component  forces,  CB  and  BA.  CB  will  then  represent  the 
force  with  which  the  wagon  presses  on  the  surface  of  the  road, 
and  AB  the  resisting  force  of  gravity  »'.  e.,  the  force  (inde- 


LOSS    OF    POWER    ON    INCLINATIONS. 


33 


pendent  of  friction)  which  resists  the  ascent  of  the  wagon,  or 
which  tends  to  drag  it  down  hill. 

To  find  the  amount  of  this  force,  from  the  two  similar  tri- 
angles, ABC  and  DEF,  we  get  the  proportion 

CA  :  AB  :  :  DE  :  EF. 

Representing  the  length  of  the  plane  by  /,  its  height  by  A, 
and  the  weight  of  the  wagon  and  load  by  W,  this  proportion 
becomes 

W  :  AB  :  :  /  :  h, 

whence  AB=W-r  ;  that  is,  the  resistance  of  gravity  due  to 

the  inclination,  is  equal  to  the  whole  weight,  multiplied  by  the 
height  of  the  plane  and  divided  by  its  length.  If  the  inclina- 
tion be  one  in  twenty,  then  this  resistance  is  equal  to  -£$  W. 

In  this  investigation,  we  have  neglected  three  trifling  sources 
of  error  :  arising  from  part  of  the  weight  being  thrown  from 
the  front  axles  to  the  hind  ones,  in  consequence  of  the  inclina- 
tion of  the  traces  ;  from  the  diminution  of  the  pressure  of 
the  weight,  owing  to  its  standing  on  an  inclined  surface  ;  and 
from  the  hind  wheels  bearing  more  than  half  of  the  pressure, 
in  consequence  of  the  line  of  gravity  falling  nearer  them. 

The  results  of  experiments  fully  confirm  the  deductions 
cf  theory  as  to  the  great  increase  of  draught  upon  incli- 
nnlions.  The  following  table  exhibits  the  force  required 
(according  to  Sir  Henry  Parnell)  to  draw  a  stage  coach 
over  parts  of  the  same  road,  having  different  degrees  of 
inclination  : 


Inclination. 

FORCE    OF    DRAUGHT    REQUIRED. 

At  6  miles  per  hour. 

At  8  miles  pei  hour. 

At  10  miles  per  hour. 

1  in    20 

268 

296 

318 

1  in    26 

213 

219 

225 

1  in    30 

165 

196 

200 

1  in    40 

160 

166 

172 

1  in  600 

'   111 

120 

128 

34  WHAT    ROADS    OUGHT    TO    BE. 

Putting  into  a  different  form  the  results  of  these  and  otlur 
experiment?,  we  establish  the  following  data: 

Calling  the  load  which  a  horse  can  draw  on  a  level,  1.00 


on  a  rise  of 


in  100  a  horse  can  draw  only  .90* 


in    50  .81* 

in    44         "         "          "  .75! 

in    40         "         "          "  .72f 

in    30         "         "          "  .64f 

in    26         "         »  "  .54f 

in    24         "         "          "  .50} 

in    20         "         "          "  .40f 

in     10         "         "          "  .25* 

In  round  numbers,  upon  a  slope  of  1  in  44,  or  120  iect 
lo  the  mile,  a  horse  can  draw  only  three-quarters  as  much 
as  he  can  upon  a  level  \  on  a  slope  of  1  in  24,  or  220  feet  to 
the  mile,  he  can  draw  only  half  as  much  ;  and  on  a  slope 
of  I  in  10,  or  528  feet  to  the  mile,  only  one  quarter  as 
much. 

This  ratio  will,  however,  vary  greatly  with  the  nature 
and  condition  of  the  road  ;  for,  although  the  actual  re- 
sistance of  gravity  is  always  absolutely  the  same  upon  the 
same  inclination,  whether  the  road  be  rough  or  smooth, 
yet  it  is  relatively  less  upon  a  rough  road,  and  does  not 
form  so  large  a  proportional  share  of  the  whole  resist- 
ance. 

Thus,  if  the  friction  upon  a  road  were  such  as  lo  require, 
upon  a  level,  a  force  of  draught  equal  to  TV  °f the  load»  tlie  total 
force  required  upon  an  ascent  of  1  in  20,  would  be  fV+'V— *V 
Here,  then,  the  resistance  of  gravity  is  two-thirds  of  the 
whole. 

If  the  road  be  less  perfect  in  its  surface,  so  that  its  friction 


•  Gayffier.     Experiments  on  a  French  road. 

t  Parnett.     Experiments  on  an   English  road  at  average  of  the  three 
velocities. 

t  Interpolations. 


LOSS    OF    POWER    ON    INCLINATIONS.  35 

:=  Jj,  the  total  force  upon  the  ascent  will  be   oV^aV;  an<1« 
here,  then,  the  resistance  of  gravity  is  one-half  of  the  whole. 

If   tho    friction    increase    to    TV,   the   total    resistance   is 
fV4"2\>  ^^r !  and  here,  gravity  is  only  one-third  of  the  whole 

We  thus  see  that  on  a  rough  road,  with  great  friction, 
any  inclination  forms  a  much  smaller  part  of  the  resist- 
ance than  does  the  same  inclination  on  a  smooth  road,  on 
which  it  is  much  more  severely  felt,  and  proportionally 
more  injurious ;  as  the  gaps  and  imperfections  which 
would  not  sensibly  impair  the  value  of  a  common  knife, 
would  render  a  fine  razor  completely  useless. 

The  loss  of  power  on  inclinations  is  indeed  even  greater 
than  these  considerations  show  ;  for,  besides  the  increase 
of  draught  caused  by  gravity,  the  power  of  the  horse  to 
overcome  it  is  much  diminished  upon  an  ascent,  and  in 
even  a  greater  ratio  .than  that  of  man,  owing  to  its  ana- 
tomical formation  and  its  great  weight.  Though  a  horse, 
on  a  level,  is  as  strong  as  five  men,  yet  on  a  steep  hill  it 
is  less  strong  than  three  ;  for  three  men,  carrying  each 
100  Ibs.,  will  ascend  faster  than  a  horse  with  300  Ibs.* 

Inclinations  being  always  thus  injurious,  are  particularly 
so,  where  a  single  steep  slope  occurs  on  a  long  line  of 
road  which  is  comparatively  level.  It  is,  in  that  case, 
especially  important  to  avoid  or  to  lessen  this  slope,  since 
the  load  carried  over  the  whole  road,  even  the  level  por- 
tions of  it,  must  be  reduced  to  what  can  be  carried  up  the 
ascent.  Thus,  if  a  long  slope  of  1  in  24  occurs  on  a  level 
road,  as  a  horse  can  draw  up  it  only  one  half  of  his  full 
load,  he  can  carry  over  the  level  parts  of  the  road  only 
half  as  much  as  he  could  and  should  draw  thereon 

This  evil  is  sometimes  partially  remedied  by  putting  on 
a  full  load  and  adding  extra  horses  at  the  foot  of  the  steep 

*  Emerson.     Mechanics. 


36  WHAT  ROADS  OUGHT  TO  BE 

slope.  Oxen  are  thus  employed  to  assist  carriages  up  the 
high  hills,  on  the  summits  of  which,  for  safety  in  time  of 
war,  the  Etruscans  built  their  cities  of  Perugia,  Cortona, 
&e.  But  this  is  an  inconvenient,  as  well  as  expensive 
system,  and  the  truest  economy  is,  to  cut  down,  or  to  go 
around  such  acclivities,  whenever  this  is  possible.* 

The  bad  effects  of  this  steepness  are  especially  felt  m 
winter,  when  ice  covers  the  road,  for  the  slippery  surface 
causes  danger  in  descending,  as  well  as  increased  labor  in 
ascending.  The  water  of  rains,  also,  runs  down  the  road 
and  gullies  it  out,  destroying  its  surface,  and  causing  a 
constant  expense  for  repairs,  oftentimes  great  enough  to 
pay  for  a  permanent  improvement. 

The  loss  of  power  on  inclinations  being  so  great  as  has 
been  shown,  it  follows  that  it  is  very  important  never  to 
allow  a  road  to  ascend  or  descend  a  single  foot  more  than 
is  absolutely  unavoidable.  If  a  hill  is  to  be  ascended,  the 
road  up  it  should  nowhere  have  even  the  smallest  fall  or 
descent,  for  that  would  make  two  hills  instead  of  one  ;  but 
it  should  be  so  located  and  have  such  cuttings  and  fillings, 
as  will  secure  a  gradual  and  uninterrupted  ascent  the 
whole  way. 

In  this  point  engineering  skill  can  make  wonderful  improve- 
ments. Thus,  an  old  road  in  Anglesea,  laid  out  in  violation  of 
this  rule,  rose  and  fell  between  its  extremities,  24  miles  apart, 
a  total  perpendicular  amount  of  3,540  feet ;  while  a  new  road 
laid  out  by  Telford  between  the  same  points,  rose  and  fell  only 
2,257  feet;  so  that  1,283  feet  of  perpendicular  height  is  now 
done  away  with,  which  every  horse  passing  over  the  road  had 
previously  been  obliged  to  ascend  and  descend  with  its  load. 
The  new  road  is,  besides,  more  than  two  miles  shorter.  Such  is 

»  In  Chapter  IV.,  under  the  head  of  "  Roads  with  Trackways,"  will  be 
described  a  valuable  palliation  of  the  evils  of  steep  ascents  in  cases  where 
they  cam  int  be  avoided 


UNDULATING    ROADS.  37 

one  of  the  results  of  the  labors  of  a  skilful  road-make/,  and  many 
such  improvements  might  be  made  in  our  American  roads 
For  a  recent  remarkable  instance,  see  page  233. 

UNDULATING    ROADS. 

There  is  a  popular  theory  that  a  gently  undulating  road 
is  less  fatiguing  to  horses  than  one  which  is  perfectly  level. 
It  is  said  that  the  alternations  of  ascent,  descent,  and  levels 
call  into  play  different  muscles,  allowing  some  to  rest  while 
the  others  are  exerted,  and  thus  relieving  each  in  turn. 

Plausible  as  this  speculation  appears  at  first  glance,  it 
will  be  found  on  examination  to  be  untrue,  both  me- 
chanically and  physiologically  ;  for,  considering  it  in  the 
former  point  of  view,  it  is  apparent  that  new  ascents  are 
formed  which  offer  resistances  not  compensated  by  the 
descents  ;  and  in  the  latter,  we  find  that  it  is  contradicted 
by  the  structure  of  the  horse.  The  question  was  submitted 
by  Mr.  Stevenson*  to  Dr.  John  Barclay  of  Edinburgh 
"  no  less  eminent  for  his  knowledge,  than  successful  as 
a  teacher  of  the  science  of  comparative  anatomy,"  ana 
he  made  the  following  reply  : — "  My  acquaintance  with 
the  muscles  by  no  means  enables  me  to  explain  how  a 
horse  should  be  more  fatigued  by  travelling  on  a  road  uni- 
formly level,  than  by  travelling  over  a  like  space  upon  one 
that  crosses  heights  and  hollows  ;  but  it  is  demonstrably 
a  false  idea,  that  muscles  can  alternately  rest  and  come 
into  motion  in  cases  of  this  kind Much  is  to  be  as- 
cribed to  prejudice  originating  with  the  man,  continually 
in  quest  of  variety,  rather  than  with  the  horse,  who,  con- 
sulting only  his  own  ease,  seems  quite  unconscious  of 
Hogarth's  Line  of  Beauty." 

Since  this  doctrine  is  thus  seen  to  be  a  mere  popular 

»  Report  on  the  Edinburgh  Railway 


38  WHAT   ROADS    OUGHT    TO   BE. 

error,  it  should  be  utterly  rejected,  not  only  because  false 
in  itself,  but  still  more  because  it  encourages  the  making 
ol  undulating  roads,  and  thus  increases  the  labor  and  cost 
of  carnage  upon  them. 

GREATEST    ALLOWABLE    SLOPE. 

A  perfectly  level  road  is  thus  seen  to  be  a  most  desira 
ble  object ;  but  as  it  can  seldom  be  completely  attained, 
we  must  next  investigate  the  limits  to  which  the  slopes  of 
a  road  should  be  reduced  if  possible  and  determine  what 
is  the  steepest  allowable  or  maximum  slope. 

This  depends  on  two  different  considerations,  according 
as  the  slope  is  viewed  as  a  descent  or  as  an  ascent,  each 
of  which  it  alternately  becomes,  according  to  the  direction 
of  the  travel. 

Viewed  as  a  descent,  it  chiefly  concerns  the  safety  of 
rapid  travelling,  and  applies  especially  to  great  public 
roads. 

Viewed  as  an  ascent,  it  chiefly  concerns  the  draught  of 
heavy  loads,  and  relates  particularly  to  routes  for  agricul- 
tural and  other  heavy  transportation. 

MAXIMUM    SLOPE,    CONSIDERED    AS    A    DESCENT. 

The  slope  should  be  so  gentle,  that  when  a  heavy  ve- 
hicle is  descending,  its  gravity  shall  not  overcome  its 
friction  so  far  as  to  permit  it  to  press  upon  the  horses. 
This  limiting  slope  corresponds  to  the  "  angle  of  repose" 
of  mechanical  science  ;  i.  e.,  the  angle  made  with  the 
horizon  by  the  steepest  plane  down  which  a  body  will  not 
slide  of  its  own  accord,  its  gravity  just  balancing  its  fric- 
tion, so  that  the  least  increase  of  slope  would  overpower 
the  resistance  of  the  friction,  and  make  the  body  descend. 
This  "angle  of  repose"  should  therefore  be  the  limit  of 


GREATEST    ALLOWABLE    SLOPE.  39 

the  slope  of  a  road,  for  on  such  an  inclination  a  vehicle 
once  set  in  motion  would  descend  with  uniform,  unaccel- 
erated  velocity.  This  angle  varies  with  the  smoothness  and 
hardness  of  the  road,  and  also  with  the  degree  of  friction 
of  the  axles  of  the  carriage.  On  the  very  best  class  of 
broken-stone  roads,  kept  in  good  order,  and  with  a  good 
carriage,  it  is  considered  by  Sir  Henry  Parnell,  from  his 
experiments,  to  be  1  in  35,  (or  151  feet  to  the  mile) 
which  should  therefore  be  the  maximum  slope  upon  the 
best  roads.*  On  such  a  slope  a  coach  may  be  driven 
down,  with  perfect  safety  and  complete  control,  at  the 
speed  of  twelve  jniles  per  hour. 

If  the  inclination  be  steeper  than  this,  the  danger  of  the 
descent  is  greatly  increased,  and  the  speed  must  be  less- 
ened. If  it  be  so  steep  that  a  carriage  cannot  be  safely 
driven  down  at  a  greater  speed  than  four  miles  per  hour, 
on  every  mile  of  such  a  slope  there  will  be  a  loss  of  ten 
minutes  of  time,  equivalent  to  two  miles  upon  a  level. 
To  avoid  such  an  inclination,  a  road-maker  would 
therefore  be  justified,  by  considerations  of  time-saving, 
in  adopting  a  level  route  three  times  as  long  as  the 
steep  one. 

V/hen  inclinations  are  reduced  to  this  limit  of  1  in  35, 
there  is  little  loss  of  power,  compared  with  a  perfect  level, 
in  either  direction  of  the  travel ;  for  the  increased  labor  of 
ascending  is  compensated  in  a  great  degree  by  the  in- 
creased ease  of  descending,  while  on  a  steeper  slope  this 
advantage  is  nullified  by  t'  0  r.ecessity  of  the  horses  holding 
back  the  carriage  to  resist  the  excess  of  the  force  of  gravity. 

*  On  such  roads  Dr.  Lardner  considers  the  angle  of  repose  to  be  as 
small  as  1  in  40  :  while  on  roads  not  well  freed  from  mud  and  dust,  the 
friction  increases  the  angle  to  1  in  30 ;  and  on  an  inferior  class  of  roads  if 
is  1  in  20,  or  even  steeper 


40  WHAT   ROADS    OUGHT    TO   BE. 


MAXIMUM    SLOPE,    CONSIDERED    AS    AN    ASCENT. 

Suppose  that  a  road  is  to  be  carried  over  a  hill,  which 
rises  100  feet  in  a  horizontal  distance  of  500  feet,  (i.  e., 
1  in  5)  and  which  cannot  be  avoided  by  any  horizontal 
circuit  within  the  limits  of  distance  indicated  on  page  28. 
The  question  which  presents  itself  is,  how  steep  can  the 
slope  of  a  road  up  the  side  of  this  hill  be  most  advanta- 
geously laid  out,  since,  by  adopting  a  zigzag  line,  the  road 
may  be  made  as  long  and  therefore  as  gentle  in  the  ascent 
as  may  be  desired  ?  The  shortest  line  would  run  straight 
up  the  face  of  the  hill,  and  this  line  would  give  the  least 
amount  of  labor  ;  but  then  this  labor  for  horses  would  be 
impossible  :  and  even  if  possible,  the  horses  could  not 
draw  up  the  whole  load  which  they  had  been  drawing  on 
the  other  parts  of  the  road,  nor  could  they  descend  it  with 
safety.  But,  on  the  other  hand,  the  road  should  approach 
this  shortest  line  as  nearly  as  other  considerations  will 
permit,  since,  if  it  should  zigzag  excessively  for  the  pur- 
pose of  lessening  the  steepness,  it  would  be  so  long  as  to 
:ncrease  unnecessarily  its  cost  and  the  time  and  labor  of 
travel  upon  it.  A  medium  and  compromise  between  these 
two  evils  must  therefore  be  found.  What  shall  it  be  ? 

Supposing  the  load  of  a  horse  on  the  level  portions  of 
the  road  to  be  as  much  as  he  can  regularly  and  constantly 
draw,  his  power  of  drawing  it  up  an  ascent  will  depend 
upon  how  much  extra  exertion  he  is  capable  of  putting 
forth.  This  is  not  very  accurately  ascertained  or  defined, 
and  depends  very  much  on  the  length  of  the  ascent,  but 
may  be  assumed  at  double  his  usual  exertion.*  Now  a 
horse  drawing  a  'oad  on  a  level  road  of  the  best  character, 

*  Gayffier,  p.  9 


GREATEST    ALLOWABLE    SLOPE.  41 

such  as  has  been  previously  considered,  is  obliged  by  the 
resistance  of  the  friction  to  exercise  against  his  collar  a 
pressure  of  about  one  thirty-fifth  of  the  load.  If  he  can 
just  double  this  exertion,  he  can  lift  one  thirty-fifth  more, 
and  the  slope  which  would  force  him  to  lift  that  proportion 
would  be  (as  was  shown  on  page  32)  one  of  1  in  35.  On 
this  slope  he  would  therefore  be  compelled  to  double  his 
ordinary  exertion,  and  on  this  supposition  it  would  be  the 
maximum  slope  allowable,  considered  as  an  ascent. 

These  two  methods  of  determining  the  maximum  slope 
(by  considering  it  as  an  ascent  and  as  a  descent)  are  en- 
tirely independent  of  each  other.*  If  they  give  different 
results,  the  smallest  one,  or  the  least  slope  obtained,  r^.ust 
be  adopted ;  for,  if  it  be  disadvantageous  to  employ  a 
slope  steeper  than  1  in  35,  it  must  a  fortiori  be  still  more 
so,  to  employ  one  steeper  than  1  in  30,  or  1  in  20  ;  though 
even  greater  slopes  are  too  often  met  with. 

Upon  most  of  our  American  roads  the  resistance  of 
friction  would  be  found  to  be  nearer  ^\  than  ^j,  and  1  in 
20  would  therefore  be  their  maximum  slope  with  their 
present  condition  of  surface.  But  as  it  is  to  be  hoped 
that  in  this  respect  they  will,  before  long,  be  greatly  im- 
proved, in  which  case  they  would  demand  more  and  more 
gentle  slopes,  we  should  anticipate  this  desirable  consum- 
mation, by  giving  in  advance  to  all  new  lines  of  road  at 
least,  if  not  to  the  faulty  old  ones,  slopes  not  exceeding  1 
in  30,  which  s.eems  to  be  a  just  medium. 

*  They  give  identical  results  in  this  case,  only  because  the  extra  exer- 
tion happened  to  be  taken  as  doubled.  Suppose  it  to  be  tripled.  The 
horse  can  lift  323  more,  which  corresponds  to  a  slope  of  1  in  17£.  Horses 
can  indeed  for  a  short  time  exercise  a  tension  of  six  times  the  usual 
amount,  but  the  above  assumption  of  double  is  more  iepeiidubto,  though  it 
^nnot  be  fixed  with  the  precision  w  hich  is  desirable. 


42  WHAT    ROADS    OUGHT  TO    BE. 

The  maximum  established  by  V 'administration  des  Fonts  el 
Chaussees,  the  French  government  board  of  engineers  of  roada 
and  bridges,  is  1  in  520.  This,  however,  was  fixed  at  a  time 
when  the  usual  surface  of  roads  was  much  inferior  to  its  pres- 
ent condition. 

The  great  Holyhead  road,  made  by  Telford  through  tho 
very  mountainous  district  of  North  Wales,  has  1  in  30  for  ils 
maximum,  except  in  two  cases,  (one  of  1  in  22,  and  a  very 
short  one*  of  1  in  17)  and  in  them  the  surface  of  the  road 
was  made  peculiarly  smooth  and  hard,  so  that  no  difficulty  is 
felt  by  loaded  vehicles  in  ascending.  On  the  old  line  of  road, 
the  inclinations  had  been  sometimes  as  great  as  1  in  6,  1  in  7,  &c . 

On  the  great  Alpine  road  over  the  Simplon  pass,  (which 
rises  to  a  height  of  a  mile  and  a  quarter  above  the  level  of 
the  sea)  the  slopes  average  1  in  22  on  the  Itilian  side,  and  1 
in  17  on  the  Swiss  side,  and  in  one  case  only  become  as  steep 
as  1  in  13. 

In  the  state  of  New  York  several  turnpike  companies  are 
limited  by  law  to  a  maximum  slope  of  "  eighteen  inches  to  a 
rod,"  i.e.  1  in  11.  But  this  limit  ought  not  to  be  even  ap- 
proached in  practice. 

On  our  "  National"  or  "  Cumberland"  road  the  slopes 
in  many  places  are  much  too  great,  and  its  superinten- 
dent, Capt.  Wever,  writes*  that  "  if  the  road  had  been 
very  considerably  elongated  in  order  to  effect  a  graduation 
at  angles  not  exceeding  three  degrees,  or  1  in  19,  (and  for 
the  maximum,  two  degrees,  or  1  in  29,  would  be  better) 
the  road  could  be  travelled  in  as  short  a  space  of  time  as 
it  now  is,  and  the  power  used  could  move  double  the  bur- 
den it  now  can  ;  thus  rendering  the  road,  for  commercial 
purposes,  doubly  advantageous." 

If  the  ascent  be  one  of  great  length,  it  will  be  advan- 
tageous to  make  steepest  the  lowest  portion  of  it,  upon 
which  the  horses  come  with  their  full  strength,  and  tc 

•  Report  to  United  States  Chief  Engineer,  1828. 


LEAST    ALLOWABLE    SLOPE.  43 

make  the  slopes  gentler  towards  the  summit  of  the  as- 
cent, to  correspond  to  the  continually  decreasing  strength 
of  the  fatigued  horses. 

MINIMUM    SLOPE. 

A  true  level  has  been  thus  far  considered  to  be  a  most 
desirable  attribute,  and  one  to  be  earnestly  sought  for,  in 
establishing  a  perfect  road.  This  principle  must  be  qual- 
ified, however,  by  the  announcement  that  there  is  a  mini- 
mum, or  least  allowable  slope,  which  the  road  must  not 
fall  short  of,  as  well  as  a  maximum  one,  which  it  must  not 
exceed.  If  the  road  were  perfectly  level  in  its  longitu- 
dinal direction,  its  surface  could  not  be  kept  free  from 
water  without  giving  it  so  great  a  rise  in  its  middle  as 
would  expose  vehicles  to  the  danger  of  overturning.  Bui 
when  a  road  has  a  proper  slope  in  the  direction  of  its 
length,  not  only  do  the  side-ditches  readily  discharge  the 
water  which  falls  into  them,  but  every  wheel-track  that  is 
made,  becomes  also  a  channel  to  carry  off  the  water. 

The  minimum  slope  (flatter  than  which  the  road  should 
not  be)  is  assumed  by  an  experienced  English  engineer 
to  be  one  in  eighty,  or  66  feet  to  the  mile.  The  minimum 
established  in  France  by  the  Corps  des  Fonts  et  Chans- 
sees  is  .008,  or  one  in  a  hundred  and  twenty-five,  or  42 
feet  to  the  mile.  An  angle  of  one-half  a  degree  is  often 
named  in  this  connection  ;.  it  equals  one  in  a  hundred  and 
fifteen.  In  a  perfectly  level  country  the  road  should  be 
artificially  formed  into  gentle  undulations  approximating 
to  the  minimum  limit. 

Finally,  then,  we  arrive  at  this  conclusion,  that  the  lon- 
gitudinal slopes  of  a  road  should  be  kept,  if  possible,  be- 
tween 1  in  30  and  1  in  1 25,  never  steeper  than  the  former, 
nor  nearer  to  a  level  than  the  latter. 


44 


WHAT  ROADS  OUGHT  TO  BE. 


TABLES  OF  :.NCLINATIONS. 

Tnere  being  three  different  methods  of  specifying  de- 
grees of  inclination,  (viz.  by  the  angle  made  with  the 
horizon,  by  the  proportion  between  the  ascent  and  the 
horizontal  distance,  and  by  the  ascent  per  mile)  it  is  fre- 
quently desirable  to  compare  the  different  expressions. 
The  following  tables  show  the  values  which  correspond  to 
each  other. 


Angles. 

Inclinations. 

Feet  per  mile. 

10 

in  115 

46 

f° 

in     76 

69 

1   ° 

in     57 

92 

H° 

in     38 

138 

2"° 

in     29 

184 

2A° 

in     23 

231 

3"° 

in     19 

277 

4  ° 

in     14 

369 

5  ° 

in     11 

462 

.    l 

Inclinations. 

Angles. 

Feet  per  mile. 

1  in     10 

5°  43' 

528 

1  in     13 

4°  24' 

406 

1  in     15 

3°  49' 

352 

in     20 

2°  52' 

264 

in     25 

2°   18' 

211 

in     30 

1°  55' 

176 

in     35 

1°  38' 

151 

in     40 

1°  26' 

132 

in     45 

1°   16 

117 

in     50 

1°     9' 

106 

in  100 

0°  35' 

53 

in  125 

0°  28' 

49 

THEIR    CROSS    SECTIONS. 


4ft 


3.    WHAT  ROADS  OUGHT  TO  BE  AS  TO  THEIR  CROSS-SECTION. 

The  cross-section  of  a  road  is  the  view  which  it  would 
present  if  cut  through  at  right  angles  to  its  length,  one  of 
the  portions  being  removed.  It  comprises  the  following 
subjects  of  investigation  : 

1.  The  width  of  the  road. 

2.  The  shape  of  the  road-bed. 

3.  Foot-paths,  $c. 

4.  Ditches. 

5.  The  side-slopes  of  the  cuttings  and  fillings. 


Fig.  3. 


The  proper  width  for  a  road  depends,  of  course,  upon 
its  importance,  and  the  amount  of  travel  upon  it.  Its 
minimum  is  about  one  rod,  or  16i  feet,  sufficient  to  enable 
two  vehicles  to  pass  each  other  with  ease.  For  ordinary 
town  roads  a  good  width  is  from  20  to  25  feet.  A  width 
of  30  feet  is  fully  sufficient  for  any  road,  except  one  which 
forms  the  approach  to  a  very  populous  city. 

Any  unnecessary  width  (such  as  is  often  adopted  in  a 
spirit  of  public  ostentation)  is  injurious,  not  only  from  its 
waste  of  land,  but  from  its  increase  of  the  labor  and  cost  of 
keeping  the  road  in  repair ;  each  rod  in  width  adding  two 
acres  per  mile  to  the  area  covered  by  the  road. 

In  the  state  of  New  York,  by  the  revised  statutes,  "All 
public  roads,  to  be  laid  out  by  the  commissioners  of  high- 
ways of  any  town,  shall  not  be  less  than  three  rods  wide." 

This  is  to  be  the  width  between  fences  ;  and  no  more 


46  WHAT    ROADS    OUGHT    TO    BE 

of  it  need  be  worked,  or  formed  into  a  surface  for  travel- 
ling upon,  than  is  deemed  necessary. 

The  same  laws  declare,  "  It  shall  be  the  duty  of  the 
commissioners  of  highways  to  order  the  overseers  of  high- 
ways to  open  all  roads  to  the  width  of  two  rods  at  least, 
which  they  shall  judge  to  have  been  used  as  public  high 
ways  for  twenty  years." 

It  is  also  ordered  that  "  all  privaie  roads  shall  not  be 
more  than  three  rods  wide." 

Turnpike-roads  are  obliged  by  the  statute  to  be  "  laid 
out  not  less  than  four  rods  wide,"  and  "  twenty-two  feet 
of  such  width  to  be  bedded  with  stone,"  &c.  When  a 
precipitous  locality  renders  the  full  width  impracticable, 
"  twenty-two  feet"  is  the  minimum  width  permitted. 

Where  a  road  ascends  a  steep  hill-side  by  zigzags, 
it  should  be  wider  on  the  curves  connecting  the  straight 
portions.  The  width  of  the  roadway  may  be  increased 
about  one-fourth,  when  th«  angle  between  the  straight 
portions  of  the  zigzags  is  from  120°  to  90°  ;  and  the  in- 
crease should  be  nearly  one-half,  when  the  angle  is  from 
90°  to  60°.* 

The  Roman  military  roads  had  their  width  established,  by 
the  laws  of  the  Twelve  Tables,  at  twelve  feet  when  straight, 
and  sixteen  when  crooked  ;  barely  sufficient  for  the  army,  bag- 
gage, and  military  machines. 

The  French  engineers  make  four  different  classes  of  roads. ] 
The  first  class  comprises  such  as  pass  from  the  capital  of 
one  country  to  that  of  another.     Their  width  is  U6  feet,  of 
which  22  in  the  middle  are  stoned  or  paved. 

Those  of  the  second  class  pass  from  the  metropolis  of  a 
country  to  its  other  great  cities.  Their  width  is  52  feet,  of 
which  20  in  the  mid  lie  are  stoned. 

Those  of  the  third  class  connect  large  towns  with  each  other 

«  Mohan,  p.  282.  t  Gayffier,  p.  90 


THEIR    WIDTH.  47 

and  with  first-class  roads.     Their  width  is  33  feet,  with  16 
feet  in  the  middle  stoned. 

The  fourth  class  contains  common  town  roads.  Their  width 
is  26  feet,  with  the  same  middle  causeway  as  the  last. 

In  England,  the  prescribed  width  for  turnpike-roads  at  the 
approach  to  populous  towns  is  60  feet.  The  limits  of  by-roads 
are,  for  carriage-roads,  20  feet ;  for  horse-roads,  8  feet ;  and 
for  foot-paths,  6£  feet.* 

TelforcTs  Holyhead  road,  a  model  road  for  a  hilly  country, 
has  the  following  width  in  the  clear  within  the  fences  :  32  feet 
on  flat  ground  ;  28  feet  when  there  are  side-cuttings  less  than 
three  feet  deep  ;  and  22  feet  along  steep  ground  and  precipices. 
The  United  Slates  National  or  Cumberland  road  has  80 
feet  in  width  cleared,  but  the  road  itself  is  only  30  feet. 

The  broken-stone  read  between  Albany  and  Troy  is  32  feet 
wide,  besides  two  sidewalks  of  8  feet  each. 

The  "  Third  Avenue"  of  the  city  of  New  York  is  60  feet 
wide  between  the  sidewalks,  each  of  which  occupies  20  feet : 
26  feet  of  its  middle  are  stoned. 

Broadway,  New  York,  is  80  feet  wide  between  the  houses, 
of  which  19  feet  on  each  side  are  occupied  by  the  foot-pave- 
ments, leaving  42  feet  for  the  carriage-way. 
When  broken-stone  roads  are  adopted,  it  is  usual,  for 
the  sake  of  a  saving  in  the  first  cost,  to  make  only  a  cer- 
tain width  or  "  causeway,"  in  the  middle  of  the  road,  of 
the  harder  material,  and  to  form  the  sides,  or  "  wings,"  of 
the  natural  earth,  (or  of  broken  stone,  if  the  causeway  be 
a  pavement)  which  will  be  preferable  in  summer  and  for 
light  vehicles  and  horsemen.!     Sixteen  feet  for  the  mid- 
dle and  twelve  for  the  sides  is  a  common  proportion. 

If  the  stoned  part  be  made  narrower  than  just  wide  enough 
for  two  carriages  to  pass  upon  it,  it  should  be  made  only  wide 

*  Roads  and  Railroads,  p.  73. 

t  A  serious  objection  to  this  plan  is,  that  the  wheels  which  cross  the 
road,  and  are  alternately  on  the  stone  and  on  the  earth,  will  deposite  earth 
upon  the  stone  surface,  to  the  great  deterioration  of  its  advantages. 


48 


WHAT    ROADS    OUGHT    TO    BE. 


enough  for  one  ;  for  any  intermediate  width  will  be  a  waste  of 
all  the  surplus  beyond  what  one  requires. 

If  the  road  is  to  he  made  wider  than  two  vehicles  require, 
(which  strictly  is  only  12  feet)  it  should  be  enlarged  at  once  to 
23  feet ;  for  any  intermediate  width  will  cause  unequal  and  ex- 
cessive wear,  and  therefore  be  false  economy  :  an  unexpected 
conclusion,  which  results  from  an  investigation  of  Gayffier, 
pages  184-8. 

It  would  be  preferable  to  place  the  harder  material  on 
the  sides  of  the  road,  instead  of  on  the  centre  ;  for  the 
drivers  of  heavily-laden  vehicles  will  generally  keep  them 
on  the  sides  of  the  road,  so  that  they  can  walk  on  the  foot- 
paths ;  and  if  this  part  be  not  of  the  hardest  material,  it 
will  soon  be  cut  up  and  rutted  by  the  heavy  wagons  fol 
lowing  each  other  in  the  same  track.* 

SHAPE    OF    THE    ROAD-BED. 

In  forming  the  road-bed,  or  travelled  part  of  the  roaA 
the  first  and  most  important  point,  in  a  flat  country,  is  t« 
raise  it  above  the  level  of  the  land  through  which  it  passes 
so  that  it  may  be  always  perfectly  free  from  water ;  a 
precaution  which  is  one  of  the  most  essential  requisites 
for  keeping  a  road  in  good  condition.  Roads  are  often 
placed  in  a  hollow-way,  (or  even  a  trench  is  dug,  when 
better  materials  are  to  be  added)  and  their  surface  is 
allowed  to  remain  so  low,  that  they  form  excellent  gutters 
to  drain  the  adjacent  fields,  at  the  expense  of  the  comfort, 
labor,  and  time  of  ^11  who  travel  them.  Even  the  best 
ditches  cannot  always  secure  them  from  the  land-springs, 
(which  will  sometimes  pass  under  the  ditches  by  fissures 
which  form  inverted  siphons)  and  the  only  effectual  means 
will  be  the  raising  of  the  surface  by  an  embankment  of 

*  Pwnell,  p.  129 


THEIR    SHAPE.  49 

two  or  three  feet.  The  excavations  for  the  ditches  should 
invariably  be  thus  applied. 

The  necessary  elevation  having  been  established,  the 
shape  of  the  road-bed,  at  right-angles  to  its  length,  or  its 
"  transverse  profile,"  must  be  decided  upon. 

The  road  must  not  be  flat,  but  must  "crown,"  or  be 
higher  in  its  middle  than  at  its  sides,  so  as  to  permit  the 
water  of  rains  to  rapidly  run  off  into  the  side  ditches.  If 
originally  flat,  it  is  soon  worn  concave,  and  its  middle 
becomes  a  pool,  if  it  be  on  level  ground  ;  or  a  water- 
course, if  it  be  on  an  inclination.  In  the  former  case,  the 
road  becomes  mud ;  in  the  latter,  the  smaller  materials 
are  washed  away,  and  the  larger  stones  left  bare.  Both 
these  evils  are  of  continual  occurrence  on  our  country 
roads,  but  may  be  easily  prevented,  by  shaping  the  road 
according  to  the  instructions  to  be  presently  given. 

The  usual,  though  improper,  shape  given  to  a  road  in 
order  to  make  it  crown,  has  been  a  convex  curve,  ap- 
proaching a  segment  of  a  circle,  or  a  flat  semi-ellipse. 
Fig.  4. 


Though  recommended  by  high  authorities,  it  is  very 
faulty,  in  consequence  of  its  slope  not  being  uniform, 
(the  proportion  between  arcs  and  versed  sines  constantly 
changing)  and  giving  too  little  inclination  near  the  middle, 
and  too  much  at  the  sides.  From  this  peculiarity  the 
following  evils  result : — 

1.  The  water  stands  on  the  middle  of  the  road,  and 
washes  away  its  sides. 

2.  It  is  worn  down  very  unequally  :  for  all  carriages,  to 
avoid  the  danger  of  overturning  on  the  steep  sides,  will 

4 


50,  WHAT    ROADS    OUGHT   TO    BE. 

take  the  middle  of  the  road,  which  is  the  only  part  of  it 
where  they  can  stand  at  all  upright ;  while  the  road  ought, 
on  the  contrary,  to  be  so  formed  as  to  induce  vehicles  to 
traverse  it  equally  and  indifferently  in  every  part. 

3.  This  excessive  travel  on  the  middle  soon  wears  it 
into  ruts  and  holes,  so  that  more  water  will  actually  stand 
upon  such  an  originally  convex  road  thai,   on  one  reason 
ably  flat. 

4.  When  carriages  are  forced  to  travel   on  the  side?, 
they  cause  great  additional  wear  to  the  road,  from  their 
constant  tendency  to  slide  down  the  sides,  owing  to  the 
oblique  angle  at  which  the  direction  of  gravity  meets  the 
surface. 

5.  As  this  sliding  tendency  is  at  right-angles  to  the  line 
of  draught,  the  labor  of  the  horses  and  the  wear  of  the 
wheels  are  both  greatly  increased. 

6.  Whenever  vehicles  are  obliged  to  cross  the  road, 
and  mount  the  central  ridge,  they  must  overcome  the 
same  resistance  of  gravity,  as  when  they  are  drawn  up  a 
longitudinal  hill. 

The  best  transverse  profile  for  a  road  on  level  grouftd, 
is  that  formed  by  two  inclined  planes,  meeting  in  the 

Fig.  5. 

centre  of  the  road,  and  having  their  angle  slightly  rounded 
by  a  connecting  curve.  The  inclinations  thus  formed  will 
be  uniform,  and  the  road  will  thus  escape  most  of  the 
evils  incident  to  the  curved  profile. 

The  degree  of  inclination  of  these  planes  will  depend 
on  the  surface  of  the  road  ;  being  greatest  where  the  roal 
is  rough,  and  lessening  with  iti  improvement  in  smooth- 


THEIR    SHAPE.  51 

ness.  It  may  also  be  somewhat  less  on  a  narrow  road 
as  the  water  will  have  a  less  distance  to  pass  over.  Its 
maximum  is  limited  by  the  inconvenience  which  an  ex- 
cessive transverse  slope  would  cause  to  carriages.  A 
proper  medium  for  a  road  with  a  broken-stone  surface,  is 
1  in  24,  or  half  an  inch  to  a  foot.  Telford,  in  his  Holy- 
head  road,  adopted  1  in  30,  or  6  inches  crown  in  a  road 
of  30  feet ;  and  McAdam  1  in  36,  and  even  1  in  60,  or  3 
inches  in  a  30  feet  road.  On  a  rough  road  the  inclination 
may  be  increased  to  1  in  20;  and  diminished^  on  a  road 
paved  with  square  blocks  to  1  in  40,  or  1  in  50. 

Up  to  these  limits  the  transverse  slope  should  increase 
.with  the  longitudinal  slope  of  the  road,  which  it  should 
always  exceed,  in  order  to  prevent  the  water  running 
too  far  down  the  length  of  the  road,  and  gullying  it  out ; 
for  the  water  of  rains  runs  off  from  the  middle  of  a  road 
in  the  diagonal  of  a  rectangle,  the  sides  of  which  are  pro- 
portioned to  the  steepness  of  the  two  slopes,  longitudinal 
and  transverse. 

If  these  slopes  be  equal,  the  rectangle  becomes  a  square, 
and  the  direction  of  the  escaping  waters  makes  un  angle  of 
45°  with  the  direction  of  the  road.  j,'j~  g 

If  the  transverse  slope  be  double  the 


longitudinal,  the  waters  in  their  di-  I  / 

agonal  course  make  an  angle  of  63£° L/ 

with  the  road,  as  in  the  figure.  If 
the  road  be  level  longitudinally,  they 
run  off  at  right  angles. 


On  a  steep  side-hill,  the  transverse  profile  should  be  a 
single  slope,  inclining  inwards  from  the  outer  edges  of  the 
road  to  the  face  of  the  hill.  The  ditch  should  be  on  the 
side  of  the  hill,  and  its  waters  be  carried  at  proper  inter- 
vals under  the  road  to  its  outside  This  form  is  particu- 


H'HAT    RP4DS    OUGHT   TO    BB. 

Rg.7. 


larly  advantageous  when  the  road  curves  rapidly  around 
the  hill,  since  it  counteracts  the  dangerous  centrifugal 
force  of  the  vehicles.  It  may,  therefore,  be  also  adopted 
on  the  curve*  of  a  road  in  embankment. 

Through  villages,  where   space  must  be  economized, 
and  the  side  ditches  dispensed  with,  the  middle  portion 
Fig.  8. 


of  the  road  is  made  to  descend  each  way  from  the  centre 
as  usual,  but  the  sides  slope  upwards  towards  the  houses. 
Two  furrows,  or  shallow  water-channels,  are  thus  formed, 
which  should  be  paved  to  a  width  of  two  feet  on  each 
side  of  their  middle.  This  form  may  also  be  used  on  a 
hill-side. 

A  frequent,  but  very  bad  shape,  is  hollow  in  its  middle, 
in  wh\eh  the  waters  run.  Its  faults  are,  that  carriages 
slide  down  towards  each  Fig.  9. 

other,  especially  in  frosty 
weather,  and  that  the 
large  stream  iu  the  mid- 
dle washes  away  the  road.  It  should  never  be  used  ex- 
cept when  the  width  is  greatly  contracted,  and  when  it  is 
absolutely  impossible  to  obtain  room  for  ditches. 


FOOTPATHS    AND    DITCHES.  53 

FOOTPATHS,  &C. 

On  each  side  of  the  carriage-way  should  be  flat  mounds, 
raised  six  inches  above  the  road.  Sods,  eight  inches  wide 
and  six  inches  thick,  should  be  laid  against  these  mounds  in 
such  a  manner  as  to  form  a  sloping  edge.  The  water  which 
falls  on  the  surface  of  the  road  runs  along  the  bottoms  of 
xhese  sods,  in  the  "  side  channels"  formed  by  them,  till  it 
passes  off  under  the  mounds  into  the  ditches.  These 
mounds,  in  a  great  road  of  thirty  feet  width,  should  be  six 
feet  wide,  and  their  surfaces  should  be  inclined  1  inch  in 
a  yard.  One  of  them  should  be  covered  with  gravel  for 
a  footpath,  and  the  other  be  sown  with  grass-seed.  Their 
general  adoption  would  greatly  increase  the  safety  of  night- 
travelling,  the  accidents  in  which  often  occur  from  running 
on  high  banks  or  into  ditches.  They  are  not  high  enough 
to  overturn  a  coach  when  one  wheel  runs  upon  them,  but 
they  indicate  at  once  that  the  carriage  is  leaving  the  road. 

Outside  of  the  footpaths  should  be  fences,  (or  hedges, 
where  the  climate  will  permit)  and  outside  of  the  fences 
should  be  the  ditches.  These  mounds,  ditches,  &CM  are 
shown  in  Fig.  3. 

DITCHES. 

The  drainage  of  a  road  by  suitable  ditches  is  one  of  the 
most  important  elements  in  its  condition.  All  attempts  at 
improvement  are  useless  till  the  water  is  thoroughly  got 
rid  of,  and  a  bad  road  may  often  be  transformed  into  a 
good  one,  by  merely  forming  beside  it  deep  ditches,  suffi- 
ciently inclined  to  carry  off  immediately  all  the  water 
which  falls  upon  it.  Even  if  the  water  does  not  stand  on 
the  surface  so  as  to  form  mud,  if  it  nitrates  from  the 
higher  land  beside  it,  and  from  springs  under  it,  and  is  not 


54  WHAT    ROADS    OUGHT   TO    BE. 

well  drained  off,  it  will  weaken  the  substratum  of  the  road 
so  as  to  render  it  incapable  of  bearing  heavy  loads,  and 
will  be  absorbed  into  the  upper  stratum  by  capillary  attrac- 
tion. If  the  road  have  a  covering"  of  broken  stones,  the 
water  penetrating  into  it  makes  them  wear  away  very  rap 
idly  by  assisting  the  vibrating  motion  of  their  fragments, 
as  lapidaries  grind  down  the  hardest  stones  by  their  own 
dust,  with  the  aid  of  water. 

•  The  ditches  should  lead  to  the  natural  water-courses  of 
the  country;  and  should,  if  possible,  have  a  minimum  slope 
of  one  in  a  hundred  and  twenty-five,  corresponding  witli 
the  "  minimum  slope"  of  the  road,  though  less  will  suffice 
if  the  bottom  be  truly  cut  and  kept  free  from  grass.  They 
should  generally  be  sunk  to  a  depth  of  three  feet  below 
the  surface  of  the  road.  Their  size  will  be  regulated  by 
their  situation,  being  greater  where  they  intercept  the  wa- 
ter from  side-hills  rising  above  the  road,  and  also  where 
the  country  is  humid.  A  width  of  one  foot  at  bottom, 
with  side-slopes  depending  on  the  nature  of  the  soil,  will 
generally  suffice.  In  wet  soils  the  ditches  should  be  so 
wide  and  deep,  that  the  earth  taken  from  them  may  be 
sufficient  to  raise  the  bed  of  the  road  between  them  three 
feet  higher  than  the  natural  surface. 

There  should  be  a'ditch  on  each  side  of  the  road  on 
level  ground,  or  in  cuttings,  and  on  the  upper  side  of  the 
road,  where  it  is  on  a  hill-side.  The  water  from  the  side 
channels  must  be  carried  into  these,  and  the  contents  of 
the  ditches  must  pass  under  the  road  to  the  natural  water- 
courses by  means  of  drains,  culverts,  &c.,  as  will  be  ex- 
plained in  Chapter  III.  under  the  head  of  "  Mechanical 
Structures." 


SIDE-SLOPES.  56 


SIDE-SLOPES  OF  THE   CUTTINGS  AND  FILLIXGS. 

These  are  designated  by  the  ratie  of  the  base  to  the 
perpendicular  of  the  right-angled  triangle,  of  which  the 

Fig.  10. 


slope  is  the  hypothenuse,  the  base  being  always  named 
first,  and  the  perpendicular  being  the  unit  of  measure. 
Thus,  if  a  cutting  of  ten  feet  in  depth  goes  out  twenty 
feet,  as  in  the  figure,  its  slope  is  said  to  be  2  to  1;  if  it 
goes  out  but  five  feet,  it  is  said  to  be  £  to  1. 

The  Slopes  of  Cuttings  or  Excavations  vary  with  the 
nature  of  the  soil,  being  made  for  economy  as  steep  as 
its  tenacity  will  permit.  Solid  rock  may  be  cut- vertically, 
or  at  a  slope  of  {  to  1 .  Common  earth  will  stand  at  1  to 
1,  or  at  1 1  to  1  ;  the  latter  is  safer.  Gravel  requires  li 
to  1.  Some  clays  will  stand  at  1  to  I  ;  while  some, 
originally  sloped  2  to  1,  have  slipped  till  they  have  as- 
sumed a  slope  of  6  to  1.  The  proper  degree  of  slope  is 
best  determined  by  observing  that  at  which  the  earth  in 
question  naturally  stands.  Heavy  clayey  earth  will  as- 
sume a  slope  of  f  to  1,  and  very  fine  dry  sand  of  nearly 
3  to  1  ;  these  are  the  extremes  in  ordinary  cases. 

Deep  cuttings  should  not,  however,  be  made  with  less 
slopes  than  2  to  1,  (even  though  they  would  stand  steeper) 
so  that  the  sun  and  wind  may  freely  reach  the  road  to 
keep  it  dry.  The  south  side  of  excavations  may  be  made 


56 


WHAT    ROADS    OUGHT   TO    BE. 


even  3  to  1,  when  the  extra  earth  can  be  profitably  useo 
in  a  neighboring  embankment. 

When  the  lower  part  of  a  cutting  is  in  rock,  and  kas  t 
steep  slope,   and 
the  upper  portion 

in    earth    has    a  ^-^if' 

much  flatter  one, 
a  wide  "  bench," 
or  offset,  should 
be  made,  where 
the  change  of 
slope  takes  place. 

The  following  Table  shows  the  angle  with  the  honzoD 
made  by  slopes  of  various  proportions  of  base  to  height. 


Slopes. 

Angles. 

1     to  1 

75°  58' 

£     to  1 

63°  28' 

£     to  1 
1     to  1 

53°     8' 

45° 

H  to  i 

38°  40' 

!{•  to  1 
If  to  1 
2     to  1 

33°  42' 
29°  44' 
26°  34' 

3     to  1 

18°  26' 

4     to  1 

14°     2' 

5     to  1 

11°  19/ 

6     to  1 

9°  27' 

Fillings  or  Embankments  have  less  variety  than  cuttings 
in  the  nature  and  condition  of  their  materials,  and  there- 
fore have  less  vanety  of  slope,  which  :s  usus.ly  1|  to  1, 
or  2  to  1  ;  though  some  clays  (which  should,  however, 
never  be  employed,  if  their  use  can  be  avoided)  require 
3  or  4  to  1,  when  more  than  four  feet  high. 


SIDE-SLOPES.  67 


CURVED     SIDE-SLOPES. 

The  customary  form  of  the  side-slopes  of  cuttings  and 
fillings — that  of  an  inclined  plane — is  not  the  form  of 
most  perfect  equilibrium  and  stability.  To  secure  this, 
the  slope  may  be  steep  near  its  top,  with  its  upper  angle 
lounded  off,  but  must  widen  out  at  its  bottom,  where  the 
pressure  is  the  greatest.  This  is  the  natural  face  which 
an  excavation  assumes  when  left  to  itself,  as  shown  in 


Fig.  1 


the  figure.  Its  top,  or  salient  angle,  becomes  convex : 
and  its  bottom,  or  re-entering  angle,  is  filled  up  into  a 
concavity,  thus  forming  a  curve  of  contrary  flexure.  If 
side-slopes  were  originally  formed  into  this  shape,  they 
would  be  much  more  permanent,  and  the  elements,  rain, 
gravity,  &c.,  would  then  work  with  man,  and  assist  the 
labors  of  art,  instead  of  destroying  them,  as  when  the 
usual  form  is  employed.  This  curve  of  stability  is  more- 
over that  of  beauty,  coinciding  with  Hogarth's  "line  of 
grace." 

This  plan  is  not  known  to  have  been  ever  put  into 
practice,  though  the  walls  supporting  a  bank,  particularly 
for  a  quay,  are  sometimes  made  concave  outwardly  ;  and 
the  dam  of  the  Croton  Aqueduct  has,  for  its  outer  profile, 
somewhat  such  a  curve  as  has  been  above  recommended 


68  WHAT    ROADS    OUGHT    TO    BE. 


.  WHAT  ROADS  OUGHT  TO  BE  AS  TO  THEIR  SUBFAOR 
QUALITIES    DESIRABLE. 

The  surface  of  a  road  ought  to  be  as  SMOOTH  and  as 
HARD  as  possible,  so  as  to  reduce  to  their  smallest  possible 
degree  the  resistances  of  elasticity,  collision,  and  friction. 

Smoothness  is  not  only  essential  to  comfort,  but  even 
more  so  to  economy  of  labor,  of  carriage-wear,  and  of  road 
wear.  Carriages  passing  over  a  smooth  road  are  not  only 
drawn  more  pleasantly,  and  with  less  exertion  of  animal 
strength,  but  also  do  much  less  damage  to  the  road,  than 
when  it  has  hollows  into  which  the  wheels  fall  with  the 
momentum  of  sledge-hammers,  each  blow  deepening  the 
hole  and  thus  increasing  the  force  of  the  next  blow. 

Hardness  is  that  property  of  a  surface  by  which  it  re- 
sists the  impression  of  other  bodies  which  impinge  upon 
it.  It  is  essential  to  the  preservation  of  smoothness,  ex- 
cept in  the  case  of  elastic  surfaces. 

RESISTANCES    TO    BE    LESSENED. 

Elasticity. — A  road  may  be  perfectly  smooth,  both  be- 
fore and  after  a  vehicle  has  passed  over  it,  but  if  it  sink 
in  the  least  under  the  passage  of  a  wheel,  this  yielding 
presents  before  the  wheel  a  miniature  hill,  up  which  the 
vehicle  must  be  raised  with  all  the  loss  of  power  demon- 
strated on  page  32.  If  the  depression  were  one  inch,  and 
the  wheel  four  feet  in  diameter,  an  inclined  plane  of  1  in 
7  would  be  formed,  and  one-seventh  of  the  entire  weight 
would  need  to  be  lifted  up  this  inch.  A  road  surface  of 
caoutchouc,  or  India-rubber,  of  the  most  perfect  smooth- 
ness, would  therefore  be  the  worst  possible  for  traction, 
though  very  pleasant  for  passengers.  The  wheels  would 


RESISTANCES    TO    BE    LESSENED.  59 

always  be  in  depressions,  and  the  horses  would  be  always 
pulling  up  hill.  An  elastic  bottom  for  a  road,  such  as 
a  boggy  substratum,  would  for  this  reason  cause  great 
waste  of  draught.  A  solid,  unyielding  foundation  is 
therefore  one  of  the  first  requisites  for  a  perfect  road. 

Collision.- -The  resistance  of  collision  is  occasioned 
by  the  hard  protuberances,  inequalities,  stones,  and  other 
loose  materials  of  a  road  against  which  the  wheels  strike, 
with  great  loss  of  momentum  and  waste  of  the  power  of 
draught ;  for  the  carriage  must  be  lifted  over  them  by  the 
leverage  of  the  wheels.  It  is,  therefore,  most  important 
that  such  obstacles  should  be  as  few  and  as  small  as  pos- 
sible, the  resistance  being  proportional  to  their  size,  as 
appears  in  the  investigation  which  follows. 

The  power  required  to  draw  a  wheel  over  a  stone  or  any  obsta- 
cle, such  as  S  in  the  figure,  may  be  thus  calculated.  Let  P  repre- 
sent the  power  sought, 
or    that   which    would 
just  balance  the  weight 
on    the    point    of    the 
stone,  and  the  slightest 
increase  of  which  would 
draw    it    over.       This 
power  acts  in  the  di- 
rection   CP    with    the 
leverage  of  BC  or  DE. 
Gravity,  represented  by 
W,  resists  in  the  direction  CB  with  the  leverage  of  BD.    The 
equation  of  equilibrium  will  be  P  X  CB  =  W  X  BD,  whence 

BD  ^CDTZBCi 

VVCB~  CD— AB- 

Let  the  radius  of  the  wheel  —  CD  =  26  inches,  and  the 
height  of  the  obstacle  =  AB  =  4  inches.  Let  the  weight  W 
=  500  Ibs.,  of  which  200  Ibs.  may  be  the  weight  of  the  wheel, 
and  300  Ibs.  the  load  on  the  axle.  The  formula  then  becomes 


60  WHAT    ROADS    OUGHT   TO    BE. 

» 

^676  —  484  13.85 

P  =  500 — •  =  500  — —  =  314.3-  Ibs.      The  pres- 

sure at  the  point  D  is  compounded  of  the  weight  and  the 

power,  and  equals  W  £?  =  500  X  ?jj  =  59  libs.,  and  therefore 
Or$  2& 

acts  with  this  great  effect  to  destroy  the  road  in  its  collision 
with  the  stone,  in  addition  to  its  force  in  descending  from  it. 
For  minute  accuracy,  the  non-horizontal  direction  of  the 
draught,  and  the  thickness  of  the  axle,  should  be  taken  into 
the  account. 

The  power  required  is  lessened  by  proper  springs  to  vehi- 
cles, by  enlarged  wheels,  and  by  making  the  line  of  draught 
ascending. 

The  resistance  produced  by  the  hollows  between  the  stones 
of  a  pavement  is  of  a  different  nature.  According  to  the  in- 
vestigations of  M.  Gerstner,  the  resistance  arising  from  such 
a  surface  is  directly  proportional  to  the  load,  to  the  square  of 
the  velocity,  and  to  the  ratio  of  the  width  of  the  cavity  to  the 
radius  of  the  wheel ;  and  inversely  proportional  to  the  width 
of  the  paving  stones. 

Friction. — The  resistance  of  friction  arises  from  the 
rubbing  of  the  wheels  against  the  surfaces  with  which 
they  come  in  contact,  and  will  always  exist,  however  the 
purface  may  be  improved.  Its  two  extremes  may  be 
seen  on  a  road  of  loose  gravel,  and  on  a  railroad.  It  is 
greatly  increased  when  the  surface  is  covered  with  mud, 
or  other  loose  material,  into  which  the  wheel  may  sink, 
and  thus  give  a  wider  contact.  The  degree  in  which 
it  is  influenced  by  the  surface,  may  be  shown  by  rolling 
an  ivory  ball  successively  over  a  carpet,  a  fine  cloth,  a 
smooth  floor,  and  a  sheet  of  ice ;  the  distances  to  which 
the  same  force  will  impel  it  over  these  surfaces  increasing 
m  the  order  in  which  they  have  been  named. 

The  surface  of  a  road  may  be  improved  by  the  various 
methods  of  diminishing  the  frictior  to  be  examined  in 


FRICTION.  61 

Chapter  IV.,  such  as  "  Macadamizing"  the  road,  or  cov- 
ering it  with  a  layer  of  finely  broken  stones  ;  paving  with 
smooth  stone  blocks ;  covering  with  planks ;  or  laying 
wheel-tracks  of  stone,  wood,  or  iron. 

The  friction  on  all  these  surfaces  is  different,  and  can 
be  determined  only  by  experiment.  The  instrument  used 
for  measuring  it  is  called  a  Dynamometer.  It  resembles 
in  principle  and  general  construction  the  "  spring-balan 
ces"  in  common  use,  in  which  the  application  of  a  weight 
compresses  a  spiral  spring,  the  shortening  of  which,  as 
shown  by  a  properly  graduated  scale,  indicates  the 
amount  of  weight  applied.  In  the  dynamometer  the 
power  takes  the  place  of  the  weight  of  the  spring-balan 
ces,  one  end  of  the  instrument  being  connected  with  the 
carriage,  and  the  other  with  the  horses,  and  the  force 
which  they  exert  to  overcome  the  friction  being  shown  by 
the  index. 

Sir  John  Macneill  has  greatly  improved  the  instrument,  by 
adapting  to  it  a  piston  working  in  a  cylinder  full  of  oil,  which 
lessens  the  vibrations  of  the  index,  and  enables  its  indications 
to  be  read  with  more  ease  and  precision.  He  has  also  added 
to  it  a  contrivance  for  making  the  instrument  itself  record  tho 
degree  of  force  exerted  at  each  moment  of  motion.  It  likewise 
registers  the  distance  passed  over,  and  the  rises  and  falls  of 
the  road.* 

This  valuable  instrument  affords  a  means  of  ascertaining 
the  exact  power  required  to  draw  a  carriage  over  any  line  of 
road  ;  it  will  thus  enable  one  line  of  road  to  be  compared  with 
another,  and  their  precise  amount  of  difference  in  case  of 
draught,  to  be  determined ;  it  win  show  the  comparative  value 
of  the  different  methods  of  improving  the  surface;  and  it  will 
enable  a  registry  to  be  kept  from  year  to  year  of  the  state  of  a 
road,  showing  where  and  how  much  it  has  improved  or  do- 

*  For  a  full  description  of  tb's  instrument,  see  Parnell,  pp.  327-347. 


62  WHAT    ROADS    OUGHT    TO    BE. 

teriorated,  and  therefore  how  judiciously,  or  the  contrary,  the 
funds  expended  on  it  have  been  applied. 

The  following  are  the  results  of  experiments  made  with  this 
instrument  on  various  kinds  of  road.  The  wagon  employed 
weighed  21  cwt.,  and  the  resistance  to  draught  was  as  fol- 
lows : — 

*  On  a  gravel  road,  laid  on  earth — per  21  cwt.,  1471bs.=  y1^ 

*  On  a  broken-stone  road,     "  65      =  -j, 

*  "         on  a  paved  foundation,  "  46     =  ^ 

*  On  a  well-made  pavement,  33      =  i\ 
f  On  the  best  stone  track-ways,  per  gross  ton,     12£   =  T-$B 
J  On  the  best  form  of  railroad,                "  8      =  ^a 

From  the  above  experiments  we  infer,  in  round  num- 
bers, taking  the  maximum  load  on  a  gravel  road  for  the 
standard,  that  a  horse  can  draw — 

On  the  best  broken-stone  road,    3    times  as  much, 
On  a  well-made  pavement,  4^  limes  as  much, 

On  the  best  stone  track-ways,     1 1     times  as  much, 
On  the  best  railways,  18    times  as  much. 

Poncelet^  gives  the  following  relations  of  the  friction  to 
the  pressure,  for  wheels  with  iron  tires  rolling  on  different 
surfaces : — 

On  a  road  of  sand  and  gravel,  Jg- 

On  a  broken-stone  road,  \  I"  ordjnary  c°ndition>  £ 
{  in  perfect  condition,      T'T 

On  a  pavement  in  good  order,  ,|  Jj  J  ^  V 

On  oak  planks  not  dressed,  ff'ff 

The  most  complete  series  of  experiments  upon  the  friction 
of  vehicles  have  been  recently  made  by  M.  Morin.\\  Some  of 
the  most  important  reeults  are  given  below,  in  a  tabular  form. 
The  fractions  express  the  relation  of  the  force  of  draught  tc 
the  total  load,  vehicles  included. 

*  Parnell,  pp.  43,  73.  t  Ibid.  p.  107. 

t  Lecount,  p.  219.  §  Mdcanique  Industrielle,  p  507. 

||  Aide-Me"moire  de  M^canique.  o.  337. 


FRICTION. 


63 


CHARACTER  OF  THE  VEHICLE.  ] 

CHARACTER  OF 

Truck. 

Carriage 

THE    ROAD. 

Cam. 

(of  SJ 

(Of  Vv^lOn*   } 

with  seau  bung 

on  .pruig.. 

New    road,    covered 

with    gravel    five 

TV 

1 

i 

1 

inches  thick, 

Solid    causeway    of 

earth,  covered  with 

TV 

TV 

TV 

TV 

gravel  l^in.  thick, 

Causeway    of   earth 

in  very  good  con- 

TV 

* 

A 

^y 

dition, 

Oaken  platform, 

TV 

fi 

TV 

Broken-stone  road. 

Walk. 

Trot. 

Walk. 

Trot. 

Very  dry  and  smooth, 

JL 

_1_ 

TV 

TV 

TV 

TV 

Moist  or  dusty, 

iV 

aV 

7T 

"3T 

With  ruts  and  mud, 

nV 

_i_ 

1_ 

TV 

iV 

I 

Deep  ruts  and  thick  ) 
mud,                        \ 

TV 

TV 

• 

T2 

TV 

TV 

rV 

Pave    i  n      \  dry' 

oV 

«v 

_IT 

VR 

JL 

* 

en  '   \  muddy,  i  -^ 

TV 

TV 

oV 

TV 

aV 

From  the  above  table  it  is  apparent  how  important  is 
the  condition  in  which  the  best-made  road  is  kept,  and 
how  greatly  the  labor  of  draught  is  increased  by  mud  or 
dust  on  its  surface.  The  character  of  the  vehicle  is  also 
seen  to  have  great  influence  on  the  degree  of  friction. 

The  principal  general  resuks,  deduced  by  M.  Morin 
from  the  elaborate  experiments  above  referred  to,  are 
given  on  the  following  page. 


64  WHAT    ROADS    OUGHT    TO    BE. 


DEDUCTIONS  FROM  MORIN  S  EXPERIMENTS. 

1.  The  resistance,  or  "  Traction,"  is  directly  propor 
tional  to  the  load,  and  inversely  proportional  to  the  diam- 
eter of  the  wheel. 

2.  Upon  a  paved,  or  a  hard  Macadamized  road,  the  re- 
sistance is  independent  of  the  width  of  the  tire  when  it 
exceeds  from  3  to  4  inches.     On  compressible  roads,  the 
resistance  diminishes  when  the  breadth  of  the  tire  in- 
creases. 

3.  At  a  walking  pace,  the  traction  is  the  same,  under 
the  same  circumstances,  for  carriages  with  springs,  or 
•without  them. 

4.  Upon  hard  Macadamized  and  upon  paved  roads,  the 
traction  increases  with  the  velocity;  the  increments  of 
traction  being  directly  proportional  to  the  increments  of 
the  velocity,  above  a  speed  of  about  2  ]•  miles  per  hour ; 
but  it  is  less  as  the  road  is  more  smooth,  and  the  carriage 
less  rigid,  or  better  hung. 

5.  Upon  soft  roads  »of  earth,  or  sand,  or  turf,  or  roads 
freshly  and  thickly  gravelled,  the  traction  is  independent 
of  the  velocity. 

6.  Upon  a  well-made  and  compact  pavement  of  hewn 
stones,  the  traction  at  a  walking  pace  is  not  more  than 
three-fourths  of  that  upon   the  best  Macadamized  road 
under  similar  circumstances  :  at  a  trotting  pace  it  is  equal 
to  it. 

7.  The  destruction  of  the  road  is  in  all  cases  greater  as 
the  diameters  of  the  wheels  are  less     and  it  is  greater  in 
carriages  without  than  w'th  springs. 


COST    AND   REVENUE    COMPARED.  65 


5.     </VHAT  ROADS  OUGHT  TO  BE  AS  TO  THEER  "OST. 

A  minimum  of  expense  is,  of  course,  highly  desirable  ; 
but  the  road  which  is  truly  cheapest  is  not  the  one  which 
has  cost  the  least  money,  but  the  one  which  makes  the 
most  profitable  returns  in  proportion  to  the  amount  which 
has  been  expended  upon  it. 

To  lessen  the  cost  of  the  construction  of  a  road,  while 
striving  to  attain  the  attributes  which  we  have  found  to  be 
desirable,  we  should  endeavor  to  avoid  the  necessity  of 
making  high  embankments,  or  deep  excavations,  or  any 
rock-cuttings;  the  cuttings  through  the  hills  should  just  suf- 
fice to  fill  up  the  valleys  crossed  ;  the  line  of  the  road  should 
be  carried  over  firm  ground  and  such  as  will  form  a  good 
surface  if  no  artificial  covering  be  used  ;  or  if  it  is  to  be 
Macadamized,  it  should  pass  near  some  locality  of  good 
stone  ;  and  it  should  be  so  located  as  to  require  but  few 
and  small  mechanical  structures,  such  as  bridges,  culverts, 
retaining  walls,  &c. 

COMPARISON    OF    COST    AND    REVENUE. 

The  more  nearly,  however,  the  road  is  made  to  ap 
proximate  towards-"  what  it  ought  to  be,"  the  more  diffi- 
cult will  it  be  to  satisfy  the  demands  of  economy.  Some 
medium  between  these  extremes  must  therefore  be  adopt- 
ed, and  the^hoice  of  it  must  be  determined  by  the  amount 
and  character  of  the  traffic  on  the  road  which  it  is  pro- 
posed to  make  or  to  improve.  For  this  purpose  an  accu- 
rate estimate  is  to  be  made  of  the  cost  of  the  proposed 
improvement,  and  also  of  the  annual  saving  of  labcr  in 
the  carriage  of  goods  and  passengers  which  its  adoption 
will  produce.  If  the  latter  exceed  the  interest  of  the  for- 


66  WHAT   ROADS    OUGHT   TO    BE. 

mer,  (at  whatever  per  centage  money  for  the  investment 
can  be  obtained)  then  the  proposed  road  will  be  "  whai 
it  ought  to  be  as  to  its  cost"  From  these  considerations 
it  will  appear  that  it  may  be  truly  cheaper  to  expend  ten 
thousand  dollars  per  mile  upon  a  road  which  is  an  impor- 
tant thoroughfare,  than  one  thousand  upon  another  road  in 
a  different  locality. 

"  How  to  estimate  the  cost  ot  a  road"  will  be  considered 
at  the  end  of  Chapter  II.,  which  treats  of  its  "  Location." 
Under  the  present  head,  we  will  examine  how  we  may 
estimate  the  probable  profits  of  a  road,  and  from  the  com- 
parison of  the  two  estimates  determine  how  much  the 
projectors  of  an  improved  road  would  be  justified  in  ex 
pending  upon  it. 

AMOUNT    OF    TRAFFIC. 

Let  us  suppose  that  it  is  proposed  to  improve  a  road  in 
any  v  ay,  whether  by  Macadamizing  its  surface,  by  short- 
ening it,  or  by  carrying  it  around  a  hill  which  it  now  goes 
over.  The  first  point  to  be  ascertained  is  the  quantity 
and  nature  of  the  traffic  which  already  passes  over  the 
line.  This  may  be  most  accurately  found  by  stationing 
men  to  count  and  note  down  all  that  passes  in  a  given 
lime  of  average  activity  ;  and  from  a  sufficient  number  of 
such  returns,  well, classified,  deducing  the  annual  amount. 

COST    OF    ITS    TRANSPORTATION. 

The  cost  of  conveying  this  amount  of  traffic  is  next  to 
be  calculated.  To  simplify  the  question,  we  will  neglect 
the  gain  in  speed,  and  consider  only  the  saving  in  heavy 
transportation.  Assume  that  over  the  road,  thirty  miles 
in  length,  50,000  tons  of  freight  are  annually  carried,  an«J 
that  the  average  friction  of  'ts  surface  (as  determined  by 
a  dynamometer)  is  ^  of  the  weight.  The  annual  force  nf 


PROFITS    OF    IMPROVEMENTS.  67 

draught  required  is  therefore  2500  tons,  or  5, 000,000  Ibs. 
If  the  average  power  of  draught  of  a  horse  at  3  miles  an 
hour  for  10  hours  a  day  be  taken  at  100  Ibs.,*  there  would 

.  5,000,000 

be  required  — - —  =  50,000  horses  working  at  3  miles 

100 

per  hour.  At  this  -rate  they  would  traverse  the  road  in 
10  hours,  or  a  working  day,  and  the  total  amount  of  labor 
would  equal  50,000  days'  work  of  a  horse,  or  $37,500, 
taking  75  cents  for  the  value  of  one  day's  work. 

PROFIT    OF    IMPROVING    THE    SURFACE. 

Suppose  now  that  .the  road  is  to  be  macadamized,  or 
planked,  or  in  any  way  to  have  the  friction  of  its  surface 
reduced  to  5V  The  total  force  of  draught  will  then  be 

50,00°.x  200°  =  2,000,000  Ibs.  =  20,000  horse  power,  at 

3  miles  per  hour,  for  30  miles,  or  10  hours  =  20,000  days' 
work  of  a  horse.  This  is  a  saving  from  the  former  amount 
of  30,000.  Taking  the  value  of  the  day's  work  of  a  horse 
at  75  cents,  $22,500  would  be  the  actual  saving  of  labor 
in  each  year,  by  the  improvement  proposed,  which  amount 
the  carriers  could  afford  to  pay,  (either  in  tolls,  or  in  ma- 

*  The  power  of  a  horse  at  different  velocities  is  very  variable,  and,  in 
spite  of  many  experiments,  is  not  yet  ascertained  with  the  precision  de- 
sirable. The  usual  conventional  assumption  is  150  Ibs.  moved  20  miles  a 
day  at  the  rate  of  2£  miles  per  hour.  This  is  equivalent  to  Watts'  horse- 
power of  33,000  Ibs.  raised  1  foot  in  1  minute.  Tredgold's  experiments 
give  125  Ibs.  moved  20  miles  a  day  at  2^  miles  per  hour.  Smeaton  gives 
100  Ibs.  moved  at  same  rate  ;  and  Hachette  128  Ibs.  Numerous  careful 
experiments  on  an  English  railway  (detailed  in  "  Laws  of  Excavation 
and  Embankment  on  Railways,"  page  105)  give  110  Ibs.  moved  19.2 
miles  per  day  at  the  rate  of  2.4  miles  per  hour.  Gayffier  (page  178)  fixes 
the  power  for  a  strong  draught-horse  at  143  Ibs.  for  22  miles  per  day  at 
2J  miles  per  hour  ;  and  for  an  ordinary  horse,  at  121  Ibs.  for  25  miles  per 
day  at  2£  miles  per  hour.  As  the  speed  of  a  horse  increases,  his  power  of 
draught  diminif'ies  very  rapidly,  till  at  last  ht  can  only  move  his  own  weight 


68  WHAT  ROA  OS    OUGHT    TO    BE. 

king  the  improvement  themselves)  for  their  diminished 
expenditure  on  horses.  If  money  were  borrowed  at  6  per 
cent.,  $375,000  would  be  the  amount  which  could  be 
expended  in  making  the  improvement,  supposing  the  data 
to  have  been  correctly  assumed.  If  the  improvement  can 
be  made  for  any  amount  less  than  this,  the  difference  will 
be  so  much  clear  gain. 

PROFIT    OF    LESSENING    THE    LENGTH. 

Next,  suppose  that  the  improvement  is  only  shortening 
the  road  a  mile,  by  a  new  location  of  part  of  it.  One- 
thirtieth  of  the  original  distance,  and  therefore  labor,  is, 

saved,  or  — '——  =  1667  days'  work  of  a  horse  =$1,250 
30 

=  interest  of  $20,833.     Add  to  this  the  amount  which  the 
construction  of  this  extra  mile  would  have  cost,  and  if  the 
proposed  improvement  can  be  made  for  the  sum  of  the 
two,  or  even  a  little  more,  it  should  be  at  once  carried  into 
effect ;  for,  besides  the  saving  in  the  original  cost  and  in 
the  annual  labor,  there  is  also  that  of  time,  and  of  the  for 
mer  cost  of  repairs  of  the  extra  mile,  which  is  now  dis 
pensed  with. 

PROFIT    OF    AVOIDING    A    HILL. 

If  the  improvement  be  avoiding  a  hill,  the  resistance 
of  gravity  is  to  be  compared  with  that  of  friction.  Sup- 
pose that  a  certain  road  ascends  a  hill  which  is  a  mile 
long,  and  has  an  inclination  of  1  in  10,  and  descends  the 
other  side  which  has  the  same  slope,  and  that  a  level  route 
can  be"  obtained  by  making  the  road  a  mile  longer.  It  is 
demanded  how  much  may  be  expended  for  this  purpose. 
Suppose  that  the  friction  on  this  road  is  y\,  and  that 
50,000  tons,  as  before,  pj.ss  over  it  annually.  On  the 
original  road  of  two  miles,  the  force  of  draught  required 


PROFITS    OF   IMPROVEMENTS.  69 

.    50,000  x  2000 
to  overcome  jnction  is  — — — — — —  =  25,000    horse 

40  X  100 

25.000  x  2 

power,  at  3  miles  per  hour,  or =  16,667  hours 

3 

for  the  2  miles  =  1 667  days'  work  of  a  horse.  To  over- 
come the  gravity  of  the  loads  on  the  inclination  of  1  in  10 

requires  ^-°0°10X  20°°  =  10,000,000  Ibs.  for  1   mile  = 

333,333  Ibs.  for  30  miles  =  3333  days'  work  of  a  horse. 
The  descent  of  a  mile  on  the  other  side  of  the  hill  is  not 
a  compensation,  for  a  horse  will  have  no  more  to  take 
down  the  descent  than  he  had  dragged  up  the  ascent. 
The  total  annual  labor  to  overcome  both  friction  and 
gravity  on  these  two  miles  is  therefore  1667  +  3333=5000 
days'  work  of  a  horse. 

Upon  the  new  road  proposed,  there  is  no  inclination  to 
overcome,  but  an  extra  mile  of  length.     The  force  of 

.  50,000x2000 
draught  upon  it  due  to  friction  is  — =  2,500,000 

Ibs.  for  3  miles  =  250,000  Ibs.  for  30  miles  =  2500  days' 
work  of  a  horse.  The  saving  of  la"bor  is  therefore 
5000  —  2500  =  2500  days'  work  of  a  horse  =  $1875  =  in- 
terest of  $31,250,  which  amount  (deducting  cost  of  repairs 
of  the  extra  mile)  may  be  expended  in  making  the  new  read. 
These  calculations  havo  been  made  for  extreme  cases, 
in  order  to  make  the  principle  more  striking,  but  the  ad- 
vantages deduced  from  them  have  fallen  short  of  the  truth, 
since  only  the  original  amount  of  traffic  has  been  consid- 
ered, while  all  experience  shows  that  this  is  very  greatly 
increased  by  any  improvement  in  the  means  of  transport 
particularly  by  the  increased  speed,  which  is  an  inciden- 
tal advantage  which  we  have  not  taken  into  account. 
This  increase  of  traffic  cannot,  however,  be  determined 


70  WHAT  ROADS    OUGHT    TO    BE. 

in  advance,  by  mathematical  calculation,  though  we  can 
readily  see  from  how  wide  a  belt  of  country  the  inhabit 
ants  might  profitably  avail  themselves  of  the  improved 
road,  and  will  do  so  eventually  ;  but  how  many  of 
them  will  at  once  profit  by  it  depends  on  considerations 
of  taste,  feeling,  and  prejudices,  which  are  beyond  the 
power  of  numbers. 

CONSEQUENT    INCREASE    OF    TRAVEL. 

To  ascertain  from  what  distances  to  the  right  or  leit  on 
either  margin,  the  improved  road  might  expect  to  attract 
trave1  to  itself  from  other  thoroughfares  by  the  cross 
roads,  the  following  course  of  reasoning  may  be  employed. 

Let  AB  be  a  portion  of  the  improved 
road,  connecting  the  points  A  and  B. 
Let  C  be  a  town  connected  with  the 
other  two  points  by  the  old  unimproved 
roads  CA  and  CB.  It  is  required  to  de- 
termine whether  the  travel  from  C  to  A 
can  with  the  least  cost  (the  cost  being 
compounded  of  time  and  labor)  go  to  A 
by  the  old  road  CA,  or  take  the  old  cross- 
road CB  to  the  nearest  point  B  of  the 
improved  road,  and  then  follow  the  latter 
to  A. 

The  first  point  is  to  ascertain  the  ratio  of  improvement  of 
the  new  road  compared  with  the  old,  or  its  ratio  of  diminution 
of  cost  of  travel.  For  simplicity  of  calculation  let  us  call 
this  ratio  two.  Denote  the  miles  in  AC  by  m,  in  AB  by  n,  and 
in  BC  by  x.  The  relative  cost  of  travel  over  the  line  AC  will 

also  be  m,  over  BC  it  will  be  T,  but  over  AB  it  will  be  only  -. 

If.  then,  x  -\ —  <  m,  it  will  cost  less  to  make  the  circuit 
from  C  to  A  thro  igh  B ;  and  both  routes  will  be  equal  in  cost 
when  *-f-  —  =  m.  In  this  calculation,  therefore,  the  hypothe- 
nnse  equals  the  perpendicular  and  half  the  base ' 


INCREASE    OF    TRAVEL. 


71 


The  preceding  method  will  decide  the  question  for  any 
one  place,  but  the  following  plan  may  be  resorted  to  for 
tne  purpose  of  marking  out  on  the  map  the  entire  area, 
from  within  which  travel  may  be  expected  to  be  attracted 
to  make  use  of  the  improved  road. 

Let  AB  repre-  Fig.  15. 

C 


\ 


sent  a  portion  of 
the  improved 
road,  lying  be- 
tween the  two 
points  A  and  B, 
at  which  cross- 
roads come  in. 
It  is  required  to 
fix  the  points 
C,  C,  D,  D,  so 

that  lines  drawn  ~D  A  D~ 

from  C  and  C  to  A,  and  from  D  and  D  to  B,  shall  define  this 
tributary  area.  BC  or  AD  is  to  be  found  in  terms  of  AB, 
i-  e.  x  in  terms  of  n. 

By  the  preceding  investigation, 

a? +  |  =  B». 

But  in  the  right-angled  triangle  ABCi 
»=;•/(*»+»'.) 

Substituting  in  first  equation,  we  get 


whence  is  obtained  the  value, 

.  =  fn. 

Therefore  from  A  and  B  set  off,  at  right  angles  to  AB,  BC, 
and  AD,  each  equal  to  J  AB  ;  join  AC  and  BD  ;  and  the  area 
included  will  be  that  within  which  it  would  cost  less  for  the 
inhabitants  to  use  the  improved  road,  though  with  increased 
distance,  than  to  pursue  the  direct  but  unimproved  road.* 


*  Lccount,  Treatise  on  Railways,  p.  12. 


72  THE    LOCATION    OF    ROAD8 


CHAPTER  II. 

THE    LOCATION    OF    ROADS. 

"  I  do  not  know  that  I  could  suggest  any  one  problem  to  be  proposed  tc 
an  engineer,  which  would  require  a  greater  exertion  of  scientific  skill  and 
practical  knowledge,  than  laying  out  a  road." — DR.  LARDNER,  in  1836. 

THE  location,  or  laying  out,  of  a  road,  consists  in  de- 
termining and  marking  out  on  the  ground  .those  points 
through  which  the  road  should  pass,  in  order  to  satisfy, 
as  nearly  as  possible,  the  requirements  of  "  what  a  road 
ought  to  be." 

These  requirements,  so  far  as  they  affect  the  location 
of  a  road,  are,  in  recapitulation,  as  follows  : 

As  to  direction — that  the  road  should  be  as  straight  as 
possible,  but.  that  straightness  should  be  considered  sub- 
ordinate to  easiness  of  grade. 

As»to  slopes — that  the  road  should  be  as  level  as  possi- 
ble ;  that  it  should  avoid  unnecessary  undulations ;  and 
that  its  slopes  should  not  exceed  1  in  30,  nor  fall  below 
1  in  125. 

As  to  cost — that  the  amount  of  excavation,  embank- 
ment, mechanical  structures,  &c.,  should  be  the  least 
which  will  make  the  road  "  what  it  ought  to  be,"  in  refer- 
ence to  the  quantity  of  traffic  upon  it. 

If  the  country  through  which  the  road  is  to  pass  should 
be  a  plain  of  uniform  surface,  a  straight  line  joining  the 
two  termini,  and  running  along  the  surface  of  the  ground 
would  satisfy  all  these  conditions  at  once.  In  most  cases 


REQUIREMENTS  OF  A  PERFECT  ROAD.        73 

however,  the  ground  is  so  uneven,  hil'y,  and  undulating, 
as  to  present  very  great  difficulties  in  the  way  of  a  propei 
location.  The  shortest  line  would  pass  over  the  tops  of 
hills  and  the  bottoms  of  valleys,  and  would  thus  be  often 
so  steep  as  to  be  impassable.  The  most  level  line  would 
often  increase  the  distance  too  much  by  its  necessary 
windings  ;  as  would  also  the  cheapest  line,  which  seeks  to 
avoid  all  cuttings  and  fillings.  It  is  generally  impossible 
to  unite  all  these  requirements,  and  to  secure  ail  the  good 
qualities  and  valuable  attributes  of  the  ideally  perfect 
road ;  and  the  best  line  will  therefore  be  a  compromise 
between  them  all.  Great  skill  is  consequently  required 
to  select  the  best  possible  line  among  these  conflicting 
claims,  and  this  skill  is  more  often  needed  in  our  new  and 
rapidly  expanding  country  than  in  England  and  other 
long-settled  regions,  where  the  lines  of  all  important  roads 
have  been  long  since  established ;  though  even  there 
many  miles  of  old  roads  are  yearly  abandoned,  and  new 
lines  substituted  for  them,  in  order  to  make  a  slight  saving 
of  distance,  or  to  diminish  the  height  to  be  overcome. 

Two  distant  points  of  departure  and  arrival  being 
given,  it  is  required  to  determine  the  best  line  for  a  road 
connecting  them. 

In  many  cases  the  best  general  route  for  the  desired 
road  can  be  determined  with  perfect  certainty  without 
going  upon  the  ground,  by  simply  examining  a  map  of 
the  district  upon  which  merely  the  courses  of  the  streams 
are  laid  down.  From  them  an  instructed  and  skilful  eye 
can  deduce  all  the  elevations  and  depressions  of  the  coun- 
try with  great  precision  and  accuracy.  To  do  this,  how- 
ever, requires  a  knowledge  of  so  much  of  Physical  Geog 
raphy  as  explains  the  manner  in  which  nature  has  dis 
posed  the  inequalities  of  the  surface  of  the  earth. 


74  THE    LOCATION    OF    ilOADS 


1.  ARRANGEMENT  OF  HILLS,  VALLEYS,  AND  WATER-COURSES. 

Hills  and  valleys  at  first  glance  appear  to  the  ignorant, 
and  even  to  the  better  informed,  to  be  utterly  without 
system,  order,  or  arrangement ;  but  they  have  in  reality 
been  disposed  by  nature  with  a  great  degree  of  symmetry, 
and  their  forms  and  positions  are  found  Jo  be  the  result 
of  the  uniform  action  of  natural  laws,  and  to  be  capable 
of  being  traced  out  and  understood  with  comparative 
ease. 

Hills  being  the  great  antagonists  and  natural  enemies 
of  the  road-maker,  he  must  endeavor  to  find  out  their  weak 
points,  and  to  learn  where  he  can  best  attack  and  pene- 
trate them,  and  most  easily  overcome  their  opposition  to 
his  improvements.  Water-courses  being  his  guides  and 
chief  assistants,  he  must  study  their  habits  and  principles 
of  action,  and  learn  what  are  the  causes  which  produce 
their  seeming  vagaries  of  direction. 

HILLS  are  most  usually  found  constituting  chains,  or 
ridges,  though  sometimes  collected  in  groups,  and  at 
others  detached,  or  isolated.  The  chains  are  usually 
made  up  of  several  parallel  ranges,  and  often  send  forth 
branches  or  spurs  in  transverse  directions.  Sometimes 
they  are  merely  the  slopes  of  a  table-land  in  which  their 
summits  merge.  To  form  a  proper  conception  of  a  range 
of  hills,  imagine,  in  the  midst  of  a  plain  an  elongated  mass 
of  the  form  of  the  roof  of  a  house.  The  two  faces  of 
this  represent  the  slopes  of  the  range  ;  their  intersection 
is  the  ridge,  their  bases  are  ihefeet,  the  distance  from  one 
foot  to  the  other  is  the  breadth,  and  from  one  extremity  to 
the  other  the  length ;  the  vertical  elevation  of  the  ridge 
obovc  either  foot  is  its  relative  height,  and  above  the  sea 


LINE    OF    GREATEST    SLOPE. 


76 


its  absolute  height.  All  water  which  falls  upon  the  slopes 
descends  thence  in  a  v»  ell-defined  track  which  corresponds 
with  the  line  of  greatest  slope,  the  direction  of  which  it  is 
therefore  important  to  determine. 


LINE    OF    GREATEST    SLOPE. 


Fig.  16. 

c 


If    the   ridge   AB   of   a      A 

range  of  hills  be  horizontal,      /Y  \  /\ 

and  its    opposite  slopes   in-    /     \  \  j     \ 

clined   planes   cutting   each  \  A \ 

other  in  that  horizontal  line, 

a  spherical  body,  allowed  to  roll  down  freely  from  any  point 
C  of  the  ridge,  will  descend  in  the  line  CD  at  right  angles  to 
the  horizontal  line  AB  ;  this  line  CD  being  its  nearest  pos- 
sible approach  to  the  vertical  line  in  which  it  tends  to  move 
in  obedience  to  the  law  of  gravity.  CD  is  therefore  the  line 
of  greatest  slope,  and  consequently  of  quickest  descent.  It  is 
this  line  which  water  tends  to  follow  in  its  search  for  the  short. 


Fig.  17. 


est  path  of  descent. 

If  the  ridge  AB  be  in- 
clined, the  path  down  which 
the  sphere  will  roll  is  no 
longer  CD  at  right  angles  to  ' 
AB,  but  another  line  CE, 
diverging  in  the  direction  of 
the  slope  of  the  ridge.  To 
determine  its  precise  posi- 
tion, from  any  point  C,  Fig. 
18,  let  fall  a  vertical  line  CV, 
and,  from  any  point  F  of  this 
vertical,  raise  a  perpendicu- 
lar to  the  plane  of  the  slope, 
meeting  it  in  E.  Draw  CE, 
and  it  will  be  the  line  of 
greatest  slope  required  ;  for 
it  is  at  the  least  possible  distance  from  the  vertical  line  CV. 


76  THE    LOCATION    OF    ROADS. 

The  same  result  might  be  otherwise  obtained  by  raising  at 
C  a  perpendicular  to  the  plane  of  the  slope,  and  from  any  point 
therein  letting  fall  a  veitical  line,  which  will  intersect  the 
slope  at  some  point  E,  which  is  to  be  joined  to  C  as  before. 

When  the  slopes  are  not  planes,  the  constructions  are  more  com- 
plicated, as  the  "  lines  of  greatest  slope"  then  become  curves.* 
The  waters  which  have  fallen  upon  the  mountain-tops 
from  time  immemorial,  have  hollowed  out  for  themselves, 
or  have  adopted  for  their  passage,  channels  which  follow 
the  lines  of  greatest  slope,  whose  directions  we  have  just 
investigated.  In  descending  the  slopes  of  a  range  of  hills, 
they  thus  form  "  principal"  valleys,  the  directions  of  which, 
as  we  have  seen,  are  perpendicular  to  the  ridge  when  it  is 
horizontal,  and,  when  it  is  inclined,  share  its  general  in- 
clination. These  streams  thus  divide  the  range  or  chain 
into  ramifications  or  branches,  having  approximately  the 
same  direction  as  themselves.  The  line  in  which  the 
opposite  slopes  of  two  of  these  adjoining  "  branches"  in- 
tersect each  other,  and  which  thus  marks  out  the  lowest 
line  of  a  valley,  is  called  a  ihalweg.\  The  foot  of  one  of 
the  opposite  slopes  which  enclose  a  valley  is  generally 
parallel  to  the  foot  of  the  other  in  all  its  sinuosities,  a 
projecting  point  of  the  one  corresponding  to  a  receding 
cavity  in  the  other.  This  symmetry  is,  however,  some- 
times replaced  by  alternate  widenings  and  contractions. 

The  main  ridge  is  cut  down  at  the  heads  of  the  streams 
into  depressions  called  gaps,  or  passes ;  the  more  ele- 
vated points  are  called  peaks.  They  are  respectively  the 
origins  of  the  valleys  and  of  the  branches  on  both  sides  of 
the  principal  slope.  In  the  gaps  are  often  found  swamps, 

•  Gayffier,  p.  3. 

t  A  German  word,  (signifying  "  the  road  of  the  valley")  which  has  been 
naturalized  in  the  French  language,  and  might  be  conveniently  added  to 
our  engineering  vocabulary  in  English 


HILLS,  VALLEYS,  AND  WATER-COURSES.  77 

fed  by  the  rain  which  falls  on  the  peaks  between  which 
they  lie.  In  these  the  streams  take  their  rise,  and  thence 
run  in  contrary  directions  down  the  opposite  slopes  of  the 
ridge.  The  intermediate  potnt,  from  which  they  start  and 
diverge,  is  called  the  culminating  point  of  the  pass. 

Thus  the  "  Notch"  of  the  White  Mountains  is  the  "  cul 
minating  point"  from  which  diverge  the  Saco  and  the  Am- 
monoosuc,  the  one  emptying  into  Long-Island  Sound  and 
the  other  into  the  Atlantic.  So,  too,  from  the  various  cul- 
minating points  in  the  Allegheny  chain,  streams  run,  on 
the  one  side  towards  the  Atlantic,  and  on  the  other  to  the 
great  lakes  and  to  the  Mississippi.  From  the  culminating 
points  of  the  Rocky  Mountains,  the  slightest  impulse  would 
turn  the  nascent  stream  either  into  the  head-waters  of  the 
Missouri  and  thence  into  the  Gulf  of  Mexico,  or  into  the 
head-waters  of  the  Columbia  and  thence  into  the  Pacific 
Ocean.  The  same  phenomena,  on  a  miniature  scale,  are 
repeated  on  every  ridge  after  every  shower. 

A  river  of  the  largest  class  marks  the  lowest  points  (or 
the  thalweg)  of  a  "  principal"  valley.  On  each  side  of  it  is 
a  bounding  ridge,  which  is  itself  pierced  by  "  secondary" 
valleys,  through  each  of  which  runs  a  stream  of  less  mag- 
nitude, its  waters  emptying  into  the  first-named  river,  of 
which  it  is  a  tributary.  The  ridges  which  form  the  val- 
leys of  each  of  these  lateral  streams  are  in  their  turn  fur- 
rowed by  valleys  of  the  third  class  ;  their  banks  by  the 
valleys  of  streams  of  still  less  importance  ;  and  so  on. 

The  "  principal"  valley  is  a  trunk,  from  which,  and 
from  one  another,  the  lesser  valley's  and  streams  ramify, 
like  the  branches  of  a  tree,  or  like  the  veins  of  the  body  • 
meeting  it  at  angles  approaching  more  nearly  to  a  right 
angle  in  proportion  as  the  ridge  of  the  slope  which  they 
furrow  approaches  to  a  l.orizontal  line. 


78 


THE    LOCATION    OF   ROADS 
Fig.  19. 


INFERENCES  FROM  THE  WATER-COURSES. 

We  thus,  see  how  an  accurate  map  of  the  streams  of  any 
district  may  enable  us  to  deduce  from  them  the  position 
of  the  valleys,  their  lowest  points,  and  the  lines  of  greatest 
slope  ;  for  with  these  the  water-courses  coincide.  The 
position  of  the  ridges  which  form  the  valleys  is  a  necessary 
corollary,  as  well  as  their  lines  of  greatest  slope. 

Having  determined  these,  we  can  profit  by  the  follow- 
ing fundamental  principles  : 

1 .  If  a  principal  ridge  is  met  by  two  secondary  ridges  at 
the  same  point,  the  point  of  meeting  is  a  maximum  of  height. 

2.  If  a  principal  ridge  is  met  by  two  thalwegs  at  the 
same  point,  the  point  of  meeting  is  a  minimum  of  height. 

3.  If  a  principal  ridge  is  met  at  the  same  point  by  a 
secondary  ridge  and  a  thalweg,  nothing  can  be  inferred.* 

The  following  examples!  show  more  in  detail  some  of 
the  inferences  which  may  be  drawn  from  the  map  : 

If,  on  any  portion  of  a  map,  the  fig.  20. 

streams  appear  to  diverge  from  any 
point,  as  A,  that  point  must  be  the 
common  source  of  the  streams,  and 
therefore  the  highest  part  of  that  re- 
gion. 

The  converse  is  likewise  true  :  if 
the  streams  all  converge  towards  some 


»  Julli«n,  u.  293. 


t  Maliaii,  p.  278. 


INFERENCES    FROM    WATER-COT.  RSES. 


79 


point,  as  B,  that  will  be  the  lowest 
spot  of  the  district  embraced  with- 
in the  map. 

If  tw«  streams  are  seen  to  flow  in 
opposite  directions  from  the  sameB 
point,  as  C,  it  may  be  inferred  that 
this  spot  is  at  the  head  of  the  respec- 
tive valleys  of  these  streams,  and 
supplies  them  with  water,  and  that  it 
must  be  fed  by  higher  ground  beside 
it ;  or,  in  other  words,  that  there  is  a 
ridge  of  hills  separating  the  heads  of 
the  two  streams,  and  that  there  is  a 
depression  or  indentation  in  this  ridge 
at  the  point  C,  which  is  therefore  the 
natural  and  proper  location  for  a  road 
connecting  the  two  valleys. 

If  two  streams  are  parallel  to  each 
other,  and  flow  in  the  same  general 
direction,  this  circumstance  simply 
indicates  that  the  ridge  which  divides 
them  has  the  same  general  inclina- 
tion and  direction  as  the  streams. 
But  if  any  of  their  smaller  tributaries 
approach  each  other  at  their  sources, 
as  at  D,  this  indicates  a  depression 
of  the  main  ridge  at  that  point,  and 
marks  it  out  as  the  lowest  and  easi- 
est spot  for  the  crossing  of  a  road, 
as  in  the  preceding  case. 

If  two  streams  have  been  flowing 
m  parallel  courses,  but  at  a  certain 
point  E  diverge  from  each  other, 


Fig, 


Fig.  24. 


'8fl  THE    LOCATION    OF    ROADS. 

that  spot  is  the  lowest  point  of  the  Fiff- 25 

ridge  between  them. 

If  two  streams  are  generally  par- 
allel in  their  courses,  but  flow  in 
opposite  directions,  the  low  points  in 
the  ridge  between  them  will  still  be 
.shown  by  the  approach  to  each  other, 
as  at  F,  of  the  branches  or  secondary 
streams  ;  or  by  the  principal  streams  approaching  each 
other  at  any  point,  as  at  G. 

Having  thus  become  acquainted,  by  the  aid  of  the 
map,  with  the.  principal  features  of  the  ground,  we  are 
prepared  to  plan,  if  not  the  precise  location  of  the  road,  at 
least  the  proper  course  for  the  preliminary  explorationi 
upon  the  ground.  Long  lines  of  road  usually  follow  the 
valleys  of  streams,  and  thus  secure  moderate  grades  and 
find  the  lowest  passes  of  the  ridges  to  be  crossed.  In  this 
way  the  Simplon  road  crosses  the  Alps,  by  ascending  the 
valley  of  the  Saltine  to  its  head,  and  then  descending  that 
of  the  Doveria.  So,  too,  the  Boston  and  Albany  railroad 
finds  an  easy  grade  from  Worcester  to  Springfield  in  the 
valley  of  the  Chickapee  river,  and  then  winds  through 
the  mountains,  up  the  valley  of  the  Westfield,  till  it 
reaches  the  head-waters  of  the.Housatonic  upon  the  other 
side  of  the  ridge.  The  Utica  and  Schenectady  railroad 
never  quits  the  valley  of  the  Mohawk.  In  short,  all  roads 
strive  to  avail  themselves  of  such  facilities.  If  they  can- 
not, and  if  the  map  shows  that  their  general  course  is. 
transverse  to  the  directions  of  the  streams,  instead  of  with 
them,  it  may  be  at  once  predicted  that  they  will  be  steep 
in  their  ascents  and  descents,  or  exceedingly  expensive 
in  their  construction. 

These  principles  having  b^CH  established,  and  all  pos- 


RECONNAISSANCE.  81 

sible  information  obtained  from  the  map,  the  Reconnazs 
sance  may  be  commenced. 


2.   RECONNAISSANCE. 

This  is  a  rapid  preliminary  survey  of  the  region  through 
which  the  road  is  to  pass,  and  is  generally  made  by  »,he 
eye  alone  without  instruments.  It  is  intended  to  be  only 
an  approximation  to  accuracy,  and  to  serve  to  determine 
through  what  points  routes  should  be  instrumentally  sur- 
veyed. The  road-maker  must  examine  the  country,  map 
in  hand,  visit  and  identify  the  points  selected  on  the  map, 
and  see  whether  his  closet  decisions  have  been  correct. 
He  must  go  over  the  ground  backward  and  forward  in  op- 
posite directions,  for  it  will  often  appear  quite  different,  and 
convey  very  dissimilar  impressions,  according  to  the  point 
from  which  it  is  viewed.  Thus,  a  hill  which  one  is  de- 
scending may  seem  to  have  a  very  easy  slope,  while  it 
may  appear  very  steep  to  one  ascending  it.  No  time  or 
labor  should  be  spared  in  these  first  explorations,  as  they 
will  save  much  expense  in  the  subsequent  surveys,  which 
in  their  turn  should  be  thoroughly  executed,  to  secure  the 
route  most  economical  in  construction.  Indeed,  the  sur- 
veyor should  become  as  perfectly  acquainted  with  the 
face  of  the  country  as  if  he  had  passed  his  hand  over 
every  foot  of  it. 

Certain  points,  called  "  ruling"  or  "  guiding"  points, 
will  be  found,  through  which  the  road  must  pass  ;  such 
as  a  low  gap  in  a  range  of  hills,  a  narrow  part  of  a  river 
suitable  for  a  bridge,  a  village,  &c.  But  a  road  which  is 
to  be  a  thoroughfare  between  two  places  of  great  trade, 
should  not  be  turned  from  its  direct  course  to  accommo- 
date a  small  town,  taxing  for  its  benefit  all  who  travel  'upon 
6 


THE    LOCATION    OF    ROADS. 


the  road.  "  The  greatest  good  of  the  greatest  number" 
is  here  the  rule.  Still  less  should  individual  interest  be 
allowed  to  operate,  and  the  general  interest  of  the  com- 
munity be  sacrificed  to  the  convenience  or  caprice  of  a 
single  person.  The  permanent  benefits  to  future  genera- 
tions should  never  be  made  subordinate  and  subservient 
to  temporary  and  personal  advantages. 

Between  these  "  ruling"  points,  the  straight  line  joining 
them  is  to  be  marked  out.  The  route  adopted  must  vi- 
brate on  each  side  of  this  line,  like  an  elastic  cord,  con 
Initially  tending  to  coincide  with  it,  except  when  deflected 
to  the  right  or  to  the  left  by  weighty  reasons,  such  as  the 
accidents  of  the  ground  supply.  Thus,  a  swamp,  which 
would  render  necessary  an  expensive  causeway,  is  a  suf- 
ficient cause  for  a  wide  deviation  of  the  road  to  avoid  it. 
The  disadvantages  of  straight  lines,  which  encounter  and 
tun  over  hills,  have  been  explained  in  the  preceding  chap- 
ter. In  the  accompanying  "  Fig.  26. 
figure  the  upper  sketch 
shows  a  plan,  or  map-  A 
view,  of  two  roads,  the 
one  ACB  over  a  hill,  and 
the  other  ADB  around  it ; 
and  the  lower  sketch 
shows  a  profile,  or  side- 
view,  of  the  respective  A 
heights  of  the  same  lines. 

When  there  are  many  small  valleys  or  ravines,  with 
projecting  spurs  and  ridges  intervening,  instead  of  making 
the  road  wind  on  the  level  ground,  and  follow  all  its  sinu- 
osities, as,  ACCCCB,  in  the  next  figure,  it  will  be  better 
to  make  a  nearly  straight  line,  as  ADDDB,  cut  through  the 
projecting  points  in  such  a  way  that  the  earth  dug  out 


RECONNAISSANCE. 


83 


shall  just  suffice  to  fill  the  hollows.     The  gain  by  saving 
of  distance  may  balance  the  cost  of  cutting  and  filling. 

Fig.  27 


When  the  route  follows  the  valley  of  a  stream,  it  may 
conform  to  its  sinuosities,  if  the  turns  are  not  too  abrupt, 
and  if  the  cuttings  and  fillings  on  a  straighter  line  would 
be  too  expensive,  but  should  approximate  to  the  lattot 
plan,  if  the  importance  of  the  road  and  the  funds  at  com- 
mand will  justify  the  increased  cost.  The  former  pl?.n, 
however,  generally  gives  the  cheapest  and  most  level 
route  ;  and  guided  by  this  principle  a  blind  man  was  for  a 
long  time  the  very  best  layer  out  of  roads  in  the  hilly  re- 
gions of  Yorkshire  and  Derbyshire.  He  followed  the 
streams  closely,  and  when  they  made  too  sharp  bends, 
he  sought  in  these  arcs  the  straightest  chords  which 
passed  over  practicable  ground. 

When  a  valley  is  to  be  crossed,  the  route  should  gen- 
erally deviate  from  the  straight  line  ACB,  (Fig.  28)  and 
curve  towards  the  head  of  the  valley  ADB,  which  there  is 
usually  shallower  and  narrower.  If  it  deviated  in  the  othei 


84 


THE    LOCATION    OF    ROADS. 


direction,  as  AEB,  it  would  Fig.  28. 

increase  the  depth  and 
width  to  be  filled  up,  as  is 
shown  by  the  correspond- 
ing profiles 

But  sometimes  the  two  A 
sides  of  the  valley  ap- 
proach each  other  at  some 
point  lower  down,  so  as 
to  render  the  space  be- 
tween their  banks  narrow- 
er though  deeper ;  and  if 
on  measurement  this  area 
is  found  on  the  whole  to  be  lessened,  so  as  to  require  less 
embankment,  the  road  should  cross  at  that  point  instead 
of  higher  up. 

Another    case    in  Fig.  29. 

which  a  valley  may, 
with  advantage,  be 
crossed  down  stream, 
is  when  in  that  part 
of  the  valley  are  found 
detached  or  isolated 
hills  and  ridges,  as  E 
and  F,  which  may 
cause  a  great  saving 
of  embankment,  on 
the  line  AEFB,  com- 
pared with  either  the 
straight  route  ACB,  or  the  up-stream  one  ADB,  as  is 
shown  in  the  accompanying  plan  and  profile,  in  which  the 
same  letters  refer  to  corresponding  lines. 

When  a  road  is  to  jam  two  places  on  the  opposite  sides 


RECONNAISSANCE.  85 

of  a  ridge,  we  can  profit  by  the  observation  that  the 
streams,  by  the  approach  of  their  sources,  show  the  low- 
est points  of  the  ridge  ;  and  of  the  various  passes  thus 
indicated,  we  should  choose  that  one,  the  valleys  of  the 
streams  from  which  run  as  nearly  as  possible  in  the  di- 
rection of  the  required  line  ;  and  that  one,  also,  which 
has  the  most  uniform  inclination — not  easy  at  the  foot 
and  steep  towards  its  summit,  as  is  often  the  case. 

When  a  road  is  to  join  two  places  situated  on  the  same 
side  of  a  mountain  ridge,  but  half  way  down  its  side,  a 
straight  line  between  them  would  cross,  in, their  deepest  and 
widest  parts,  all  the  "  principal"  valleys  which  run  down 
from  every  gap.  One  of  two  other  plans  must  then  be 
adopted  ;  either  to  ascend,  and  carry  the  road,  with  neces- 
sary windings,  at  the  level  of  the  culminating  points  of 
the  gap,  where  the  valleys  have  only  begun  to  be  hollowed 
out ;  or  to  carry  it  at  the  foot  of  the  ridge,  where  the  val- 
leys have  run  out  to  nothing,  and  merged  themselves  un- 
distinguishably  in  the  plain.  Either  plan,  in  spite  of  the 
initial  and  final  ascent  and  descent,  is  preferable  to  the 
direct  line. 

Fig.  30. 

D 


~T 

The  respective  profiles  of  the  three  plans  would  be 
somewhat  as  represented  in  the  figure,  in  which  ACB  is 
the  first  plan,  ADB  the  second,  and  AEB  the  last.  The 
last  line  is  generally  taken,  because  there  are  more  inhab- 
itants at  the  foot  of  the  ridge.  It  would  properly  run  near 
the  line  of  separation  between  the  uncultivated  slopes  and 
the  ploughed  fields. 


86  THE    LOCATION    OF    ROADS. 

.The  location  of  a  road  is  also  influenced  by  the  geology 
of  a  district,  which  must  therefore  be  carefully  studied 
This  science  will  make  known  the  probability  of  finding 
rock  on  cutting  deep  into  a  hill  proposed  to  be  crossed  ; 
in  which  case  the  cutting  should  be  avoided,  if  possible, 
by  a  different  location  of  the  line.  It  will  also  determine 
the  dips  of  the  strata  to  be  cut  into,  the  angle  at  which 
they  will  stand,  and  their  liability  to  slip  ;  and  therefore 
through  which  the  line  may  best  pass.  If  the  road  is  to 
be  covered  with  broken  stone,  or  to  be  paved,  a  know- 
ledge of  the  locality  of  the  best  materials  might  cause  a 
line  approaching  it  to  be  preferred  to  one  which  left  it  at 
a  distance. 

The  Reconnaissance  is  to  be  made  in  accordance  with 
the  principles  which  have  been  enunciated,  obtaining  all 
needful  information  from  the  residents  of  the  region  to  be 
examined,  and  the  details  of  its  general  course  are  to  be 
marked  out  on  the  ground,  thus  establishing  "  Approxi- 
mate" or  "  Trial"  lines.  In  a  wooded  country  this  is  done 
by  "  blazing"  the  trees  in  the  line  selected,  (removing  a 
chip  from  their  sides  with  an  axe  ;)  and  in  a  cleared  coun- 
try by  driving  stout  stakes  at  the  most  important  points  of 
the  line,  such  as  all  changes  in  its  direction,  and  in  the 
slope  of  the  ground. 

3.    SURVEY  OF  A  LINE, 

When  the  different  portions  of  a  proposed  line  have 
been  thus  marked  out,  in  order  to  form  an  accurate  opin- 
ion of  its  merits,  it  is  necessary  to  measure — 

1.  Its  distances. 

2.  Its  directions. 

3.  Its  heights 


MEASUREMENT    OF    DISTANCES.  87 

MEASUREMENT    OF    DISTANCES. 

The  length  of  a  straight  line,  that  is,  the  distance  be- 
tween its  extremities,  may  be  approximately  estimated  in 
a  variety  of  ways,  without  the  delay  of  actual  measure 
ment  in  detail. 

Sound  is  a  well-known  means.  Its  velocity  is  1100 
feet  per  second  at  the  temperature  of  freezing.*  If  a  gun 
be  fired  by  an  assistant  at  one  end  of  a  line,  an  observer 
at  the  other  end,  by  counting  the  seconds  which  intervene 
between  seeing  the  flash  and  hearing  the  report,  and  mul- 
tiplying their  number  by  1100,  can  estimate  the  distance 
with  considerable  accuracy.  If  he  have  not  a  watch  with 
a  second-hand,  he  can  at  once  make  a  portable  pendulum, 
by  fastening  a  pebble  to  a  string,  and  making  it  swing  in 
regular  vibrations,  each  of  which  will  be  performed  in  an 
exact  second,  if  the  string  be  391  inches  long ;  in  half  a 
second,  if  it  be  9f  inches  long ;  and  in  a  quarter  second, 
if  its  length  be  2|  inches. 

This  method  is  best  adapted  for  considerable  distances, 
in  which  there  are  good  points  for  observation,  such  as 
the  hills  on  the  two  opposite  sides  of  a  wide  valley. 

For  shorter  distances,  the  distinctness  with  which  dif- 
ferent objects  can  be  seen,  is  an  approximate  guide.  Thus 
the  windows  of  a  large  house  can  generally  be  counted  at 
the  distance  of  3  miles  ;  men  and  horses  can  just  be  per- 
ceived as  points  at  about  1^  miles  ;  a  horse  is  clearly  dis- 
tinguishable at  |  mile  ;  the  movements  of  a  man  at 
£  mile  ;  and  a  man's  head  is  plainly  visible  at  \  mile.f 

*  For  each  degree  of  Fahrenheit  above  32°,  add  one-half  foot,  and  for 
each  degree  below,  subtract  one-half  foot  A  temperature  of  GO0  would 
therefore  give  1100 -f-2^8  =  1114  feet  per  second. 

t  Frome,  p.  60. 


88  THE    LOCATION    OF    RC  ADS. 

-The  Arabs  of  Algeria  define  a  mile  as  "  the  distance  at 
which  you  can  no  longer  distinguish  a  man  from  a  wo- 
man." These  distances  of  visibility  will  of  course  vary 
somewhat  with  the  state  of  the  atmosphere,  and  still  more 
with  individual  acuteness  of  sight,  but  each  person  can 
modify  them  for  himself. 

For  still  less  distances,  an  easy  method  is  to  prepare 
a  scale,  by  marking  off  on  a  pencil  what  length  of  it,  when 
it  is  held  off  at  arm's  length,  a  man's  height  appears  to 
cove'r  at  different  distances  (previously  measured  with  ac- 
curacy) of  100,  500,  1000  feet,  &c.  To  apply  this,  when 

Fig.  31. 


a  man  is  seen  at  any  unknown  distance,  hold  up  the  pen- 
cil at  arm's  length,  making  the  top  of  it  come  in  the  line 
from  the  eye  to  his  head,  and  placing  the  thumb  nail  in 
the  line  from  the  eye  to  his  feet.  The  pencil  having  been 
previously  graduated  by  the  method  above  explained,  the 
portion  of  it  now  intercepted  between  these  two  lines  will 
indicate  the  corresponding  distance. 

If  no  previous  scale  have  been  prepared,  and  the  dis- 
tance of  a  man  be  required,  take  a  foot-rule,  or  any  meas- 
ure minutely  divided,  hold  it  off  at  arm's  length  as  before, 
and  see  how  much  a  man's  height  covers.  Then  know 
ing  the  distance  from  the  eye  to  the  rule,  a  statement  by 
the  Rule  of  Three  (on  the  principle  of  similar  triangles 
will  give  the  distance  required.  Suppose  a  man's  height, 
of  70  inches,  to  cover  1  inch  of  the  rule.  He  is  then  70 
times  as  far  from  the  eye  as  the  rule  ;  and  if  its  distance 


MEASUREMENT    OF    DISTANCES.  89 

be  2  feet,  that  of  the  man  is  140  feet.  Instead  of  a  man's 
height,  that  of  an  ordinary  house,  of  an  apple-tree,  the 
length  of  a  fence-rail,  &c.,  may  be  taken  as  the  standard 
of  comparison. 

Quite  an  accurate  measurement  of  a  line  of  ground  may 
be  made  by  walking  ovet  it  at  a  uniform  pace,  and  count- 
ing the  steps.  It  is  better  not  to  attempt  to  make  each 
of  the  paces  three  feet,  but  to  take  steps  of  the  natural 
length,  and  to  ascertain  the  value  of  each  by  walking 
over  a  known  distance,  and  dividing  it  by  the  number  of 
paces  required  to  traverse  it.  An  average  length  is  32 
inches.  An  instrument,  called  a  pedometer,  has  been 
contrived,  which  counts  the  steps  taken  by  one  wearing 
it,  without  any  attention  on  his  part.  It  is  attached  to  the 
body,  and  a  cord,  passing  from  it  to  the  foot,  at  each 
step  moves  a  toothed  wheel  one  division,  and  some  inter- 
mediate wheelwork  records  the  whole  number  upon  a  dial. 

These  methods  are  all  approximations.  For  more  ac- 
curate measurements  a  chain  is  employed.  The  usual  sur- 
veyor's or  Gunter's  chain,  is  66  feet  or  four  rods  long,  and 
is  divided  into  100  links  ;  but  for  the  measurement  of 
distances  only,  without  reference  to  areas  in  acres,  a  chain 
of  50  or  100  feet  is  much  preferable. 

When  obstacles  are  encountered  on  the  line,  rendering 
a  direct  measurement  impossible,  such  as  a  house,  a 
pond,  a  river,  &c.,  resort  must  be  had  to  some  of  the 
many  ingenious  contrivances  to  be  found  in  the  special 
treatises  on  surveying  and  engineering  field-work.  Two 
only  of  the  best,  which  have  the  advantage  of  requiring 
no  calculations,  will  be  here  given. 

When  the  obstacle  is  one  around  which  we  can  pass, 
such  as  a  house  or  a  pond,  the  following  plan  may  be 
adopted.  Let  AB  be  the  distance  required.  Measure 


90 


THE    LOCATION    OF    ROADS. 


Fig.  32 


from  A.  obliquely  to  some  point  C, 
past  the  obstacle.  Measure  on- 
ward in  the  same  line,  till  CD  is  as 
long  as  AC.  Place  stakes  at  C 
and  I).  From  B  measure  to  C, 
and  from  C  measure  onward  in  the 
same  line,  till  CE  is  equal  to  CB. 
Measure  ED,  and  it  will  be  equal 
to  AB,  the  distance  required. 

When  the  obstacle  is  a  river,  the  following  is  the  method 
to  be  employed.     Let  AB  be  Fig.  33. 

the  required  distance.  From 
A  measure  any  line  diverging 
from  the  river,  as  AD,  and 
set  a  stake  in  its  middle  point 
C.  Take  any  point  E,  in  the 
line  of  A  and  B.  Measure  from 
E  to  C,  and  onward  in  the 
same  line,  till  CF  equals  CE. 
Then  find  by  trial  the  point 
G,  which  shall  be  at  the  same  Q  > 
time  in  the  line  of  C  and  B,  and  in  the  line  of  D 
and  F.  Measure  the  distance  from  G  to  D,  which 
will  equal  the  required  distance  from  A  to  B.  The 
lines  which  it  is  not  necessary  to  measure  are  dotted 
in  the  figure. 


MEASUREMENT    OF    DIRECTIONS. 

Having  measured  the  lengths  of  the  various  portions  of 
the  line,  by  whatever  method  will  give  the  degree  of  ac- 
curacy required,  their  directions  are  also  to  bo  examined, 
determined,  and  recorded. 


MEASUREMENT    OF    DIRECTIONS.  91 

These  directions  may  be  accurately  determined,  with 
reference  to  the  adjoining  portions  of  the  lines,  and  there- 
fore to  any  given  line,  by  simple  measurements  with 
the  chain,  without  the  use  of  any  of  the  usual  complicated 
angular  instruments. 

Let  AB  and  BC  rep-  Fig.  34. 

resent  two  lines  on  the     .  n  .    n 

ground,  meeting  at  any 
angle.  It  is  required  to 
determine  the  change 
in  the  direction  of  the  line  BC  from  that  of  AB,  i.  e.,  the 
angle  CBD,  or  the  "  angle  of  deflection."  Set  off  from  B 
equal  distances,  BC  on  the  new  line,  and  BD  on  AB  pro- 
duced, and  measure  DC,  which  is  the  chord  of  the  angle 
required.  To  find  the  angle  numerically,  take  half  this 
measured  chord,  (which  equals  the  sine  of  half  the  angle 
to  radius  BC)  and  divide  it  by  BC.  Find  in  a  table  of 
natural  sines  the  angle  corresponding  to  the  quotient. 
Twice  this  is  the  angle  CBD  required.  But  even  this 
brief  calculation  is  needless  for  putting  down  the  line 
upon  paper,  as  it  is  only  necessary  to  describe  an  arc 
from  B  as  centre  with  BC  as  radius,  and  to  set  off  CD  of 
the  proper  length,  the  distances  being  taken  from  any  one 
scale. 

If  the  direction  of  a  line  be  required  independently  of 
any  other  line  upon  the  ground,  it  is  usually  referred  tc 
the  direction  of  the  meridian,  i.  e.,  the  line  which  passes 
through  the  north  and  south  poles  of  the  earth.  Tho 
compass  is  the  readiest  means  of  obtaining  this,  although, 
in  addition  te  its  other  inherent  defects,  it  gives  the  angle 
made  by  the  given  line  with  only  the  magnetic  meridian 
which  is  constantly  changing,  and  from  which  the  tru 
meridian  in  most  places  varies  considerably. 


THE    LOCATION    OF    ROADS. 


To  determine  the  true  meridian  (and  therefore  the 
angle  which  any  line  makes  with  it)  without  the  use  of 
the  compass,  the  following  is  a  simple  and  sufficiently 
accurate  method.  On  the  south  side  of  any  level  surface 
erect  an  upright  staff,  shown,  Fig.  35. 

in  horizontal  projection,  at  A. 
Two  or  three  hours  before 
noon  mark  the  extremity,  B, 
of  its  shadow.  Describe  an 
arc  of  a  circle  with  A,  the 
foot  of  the  staff,  for  centre, 
and  AB,  the  distance  to  the 
extremity  of  the  shadow,  foi 
radius.  At  about  as  many 
hours  after  noon  as  it  had  been  before  noon  when  the 
first  mark  was  made,  watch  for  the  moment  when  tfee  end 
of  the  shadow  touches  the  arc  at  another  point  C.  Bisect 
the  arc  BC  at  D.  Draw  AD,  and  it  will  be  the  true  me- 
ridian, or  north  and  south  line,  required. 

For  greater  accuracy,  describe  several  arcs,  mark  the 
points  in  which  each  of  them  is  touched  by  the  shadow, 
bisect  each,  and  adopt  the  average  of  all.  The  shadow 
will  be  better  defined,  if  a  piece  of  tin  with  a  hole  through 
it  be  placed  at  the  top  of  the  staff,  as  a  bright  spot  will 
thus  be  substituted  for  the  less  definite  shadow.  Nor 
need  the  staff  be  vertical,  if  from  its  summit  a  plumb- 
line  be  dropped  to  the  ground,  and  the  point  which  this 
strikes  be  adopted  as  the  centre  of  the  arcs,  through  which 
the  meridian  line  AD  is  finally  to  be  drawn.* 


*  For  the  method  of  determining  the  true  meridian  by  the  north  star 
other  method?,  see  Gillespie's  Land  Surveying,  pp.  190-198. 


MEASUREMENT    OF    HEIGHTS. 


MEASUREMENT    OF    HEIGHTS. 

The  relative  heights  of  the  different  points,  at  which 
the  line  changes  its  slope,  are  next  to  be  determined 
The  operation  required  for  this  purpose  is  called  LEVEL- 
LING. It  consists  in  finding  how  much  each  of  these 
points  is  below  any  level  line.  The  difference  of  their 
distances  below  it  (measured  perpendicularly  to  it)  is  the 
difference  of  their  heights.  The  first  step,  then,  is  to 
discover  means  of  getting  a  level  line  at  any  point  desired 

The  principle,  that  a  level  line  is  everywhere  perpen- 
dicular to  the  direction  of  gravity,  furnishes  the  first 
method.  Upon  it  depends  the  well-known  "  Mason's 
level,"  in  which  a 
straight  edge  AB  is 
"  level,"  or  horizontal, 
when  a  line  CD,  ex- 
actly at  right  angles 
to  it,  is  covered  by  a 
plumb-line  attached  to 
its  upper  extremity  C. 

As  this  position  of  the  level  line  is  inconvenient,  in 
practice,  for  long  sights,  by  inverting  the  instrument  we 
get  the  "  Plumb-line  level."  To  construct  it,  at  the  mid- 
dle of  a  straight  edge,  at- 
tach  a  bar,  so  that  a  line 
drawn  through  its  middle 
is  exactly  at  right  angles  to 
the  straight  edge.  From 
the  point  of  meeting  sus- 
pend a  plumb-line.  Turn 
the  instrument  till  the 
plumb-line  covers  the  line  drawn  on  the  bar.  Then  will 


Fig.  37. 


04 


THE    LOCATION    OF    ROADS. 


the  straight  edge  be  ja.  level  line,  and  by  looking  over  its 
surface,  or  across  sights,  placed  at  equal  heights  above  its 
ends,  this  level  line  may  be  produced  by  the  eye,  so  as  to 
pass  over  any  point  to  which  the  straight  edge  is  directed. 

A   modification    of    the  Fig.  38. 

plumb-line  level,  which 
has  the  advantage  of  be- 
ing self-adjusting,  is  call- 
ed the  "  Pendulum  lev- 
el" As  before,  a  straight 
edge  and  a  bar  are  fixed 
at  right  angles  to  each 
other,  but  a  heavy  weight  at  the  lower  extremity  of  the 
bar  keeps  it  always  vertical,  and,  consequently,  the 
straight  edge  always  horizontal.  The  whole  apparatus 
is  suspended  by  a  ring  from  the  junction  of  three  legs 
which  move  on  pivots,  so  as  to  form  a  steady  support  on 
the  most  uneven  ground.  A  "  tripod"  of  this  sort  is  gen- 
erally employed  for  the  support  of  all  the  instruments  of 
surveying. 

The  "  A  level"  is  a 
portable  and  conveni- 
ent modification  of  the 
mason's  level.  The 
legs  AB,  AC  turn  on  a 
hinge  at  A,  as  does  the 
bar  DE  at  E,  so  that  all 
three  may  be  folded  up 
into  a  stout  rod.  When 
the  plumb-line  corre- 
sponds with  the  middle  of  the  bar  DE,  the  feet  of  the  in 
strument  are  on  the  same  level  At  F  and  G  are  fixed 
two  sights,  at  equal  distances  from  the  feet,  so  that 


Fig.  39. 


LEVELLING    INSTRUMENTS. 


95 


~s. 


when  the  latter  are  level,  the  line,  obtained  by  looking 
through  these  sights,  is  level  also.  The  use  of  the  other 
divisions  on  the  bar  DE  will  be  explained  under  the  head 
of  "  Grades."* 

Another  simple  instrument  depends  upon  the  principle 
that  "  water  always  finds  its  level."  If  a  tube  be  bent  up 
at  each  end,  and  nearly  filled  with  water,  the  surface  of 
the  water  in  one  end  will  always  be  at  the  same  height  as 
that  in  the  other,  however  the  position  of  the  tube  may 
vary.  On  this  truth  depends  the  "  Water  level."  It 
may  be  easily  con-  Fig.  40. 

structed  with  a 
lube  of  tin,  lead, 
copper,  &c.,  by 
bendingup,  at  right 
angles,  an  inch  or 
two  of  each  end. 
In  these  ends  ce- 
ment thin  vials, 
with  their  bottoms 
broken  off,  so  as  to  leave  a  free  communication  between 
them.  Fill  the  tube  and  the  vials,  nearly  to  their  top, 
with  colored  water.  Cork  their  mouths,  and  fit  the  instru- 
ment, by  a  steady  but  flexible  joint,  to  a  tripod. 

To  use  it,  set  it  in  the  desired  spot,  place  the  tube  by 
eye  nearly  level,  remove  the  corks,  and  the  surfaces  of 
the  water  in  the  two  vials  will  come  to  the  same  level. 
Looking  across  them,  we  get  the  level  line  desired 
Sights  of  equal  height,  floating  on  the  water,  and  rising 
above  the  tops  of  the  vials,  would  give  a  better-defined  line. 

The  "Spirit  level"  consists  essentially  of  a  curved  glass 


See  Simms  on  Drawing  Instruments,  2d  edition,  p.  146. 


96  THE    LOCATION    OF    ROADS. 


tube  filled  with  alcohol,  but  Fig.  41. 

with  a   bubble   of  air  left 
within,  which  always  seeks 


the  highest  spot  in  the  tube,  and  will  therefore  by  its 
movements  indicate  any  change  in  the  position  of  the 
tube.  To  prepare  the  tube  for  use,  it  is  placed  with  its 
convexity  uppermost,  and  supported  either  in  a  block,  or  by 
suspension  ;  and  when  the  bottom  of  the  block,  or  the 
sights  at  each  end  of  it,  coincide  with  some  level  line 
previously  established,  marks  are  made  on  the  tube  at  the 
extremities  of  the  air  bubble.  The  instrument  is  then 
ready  for  use  ;  for  whenever  the  bubble,  by  raising  or 
lowering  one  end,  has  been  brought  to  stand  between  the 
original  marks,  (or,  in  case  of  expansion  or  contraction,  at 
equal  distances  on  either  side  of  them)  the  sights  will  be 
on  the  same  level  line. 

When,  instead  of  the  sights,  a  telescope  is  made  parallel  to 
the  level,  and  various  contrivances  to  increase  its  delicacy  and 
accuracy  are  added,  the  instrument  becomes  the  engineer's 
spirit-level,  and  is  out  of  the  reach  of  the  unprofessional  read- 
ers for  whom  this  volume  is  chiefly  designed.*  The  same  is 
the  case  with  the  "  French  reflecting  level." 

By  whichever  of  these  various  means  a  level  line  haa 
been  obtained,  the  subsequent  operations  in  making  use 
of  it  are  identical.  Since  the  "  water  level"  is  easily 
made  and  tolerably  accurate,  we  will  suppose  it  to  be  em- 
ployed. Let  A  and  B  represent  the  two  points,  the  differ- 
ence of  the  heights  of  which  is  required.  Set  the  instru- 
ment on  any  spot  from  which  both  the  points  can  be  seen, 
and  at  such  a  height  that  the  level  line  will  pass  above  the 
highest  one.  At  A  let  an  assistant  hold  a  staff  graduated  into 
feet,  tenths,  &c.  Turn  the  instrument  towards  the  staff 

*  For  its  description  and  adjustments,  see  Gillespie's  Levelling,  Part  I.,  ch&pt 
IV. 


LEVELLING. 


look  along  the  level 
line,  and  note  what 
division  on  the  staff 
it  strikes.  Then 
send  the  staff  to  B, 
direct  the  instru- 
ment to  it,  and  note 
the  height  observed 
at  that  point.  If 
the  level  line  pro- 
duced by  the  eye 


Fig.  42. 


2  feet  above  A  and  6  feet 
above  B,  the  difference  of  their  heights  is  4  feet.  The 
absolute  height  of  the  level  line  itself  is  a  matter  of 
indifference.  If  the  height  of  another  point,  C,  not  visible 
from  the  first  station,  be  required,  set  the  instrument  so  as 
to  see  B  and  C,  and  proceed  exactly  as  with  A  and  B. 
If  C  be  found  to  be  3  feet  above  B,  it  will  be  4  —  3  =  1 
foot  below  A.  If  C  be  1  foot  below  B,  as  in  Fig.  43,  it 
will  be  4  +  1—  5  feet  below  A.  The  comparative  heights 
Fig.  43 


of  a  series  of  any  number  of  points,  can  thus  be  found  in 
reference  to  any  one  of  them. 

The  beginner  in  the  practice  of  levelling  may  advan 

7 


93 


THE    LOCATION    OF    ROADS. 


.ageously  make  in  his  'field-book"  a  sketch  of  the  heights 
noted,  and  of  the  distances,  putting  down  each  as  it  is 
observed,  and  imitating,  as  nearly  as  his  accuracy  of  eye 
will  permit,  their  proportional  dimensions.*  But  when 
the  observations  are  numerous,  they  should  be  kept  in  a 
tabular  form,  such  as  that  which  is  given  below.  -The 
names  of  the  points,  or  "  stations,"  whose  heights  are  de 
manded,  are  placed  in  the  first  column  ;  and  their  heights, 
as  finally  ascertained,  in  reference  to  the  first  point,  in  the 
last  column.  The  heights  above  the  starting  point  are 
marked  +,  and  those  below  it  are  marked  — .  The  back- 
sight to  any  station  is  placed  on  the  line  below  the  point 
to  which  it  refers.  When  a  back-sight  exceeds  a  fore- 
sight, their  difference  is  placed  in  the  column  of  "  as- 
cents ;"  when  it  is  less,  their  difference  is  a  "  descent." 
The  following  table  represents  the  same  observations  as 
the  preceding  sketch,  and  their  careful  comparison  will  ex- 
plain any  obscurities  in  either. 


Stations. 

Distances 

Back-sights. 

Fore-sights. 

Ascents. 

Descents. 

Total  Heights. 

A 
B 
C 
D 
E 
F 

100 
60 
40 
70 
50 

2.00 
3.00 
2.00 
6.00 
2.00 

6.00 
4.00 
1.00 
1.00 
6.00 

+  1.00 
+5.00 

—  4.00 
—  1.00 

—  4.00 

0.00 
—  4.00 
—  5.00 
—  4.00 
+  1.00 
-3.00 

I 

15.00 

18.00 

—  3.00 

The  above  table  shows  that  B  is  4  feet  below  A  ;  thai 
C  is  5  feet  below  A ;  that  E  is  1  foot  above  A ;  and  so 
on.  To  test  the  calculations,  add  up  the  back-sights 


*  ID  the  figure,  the  limits  of  the  page  have  made  it  necessary  to  con- 
tract the  horizontal  distances  to  one-tenth  of  their  proper  proportional  size 


LEVELLING.  99 

and  fore-sights.     The  difference  of  the  sums  should  equal 
the  last  "  total  height."* 

The  level  line  obtained  by  any  of  these  instruments 
is  a  tangent  to  the  surface  of  the  earth,  and  therefore  di- 
verges from  the  surface  of  standing  water,  which  presents 
a  curve  corresponding  to  that  of  the  earth.  The  differ- 
ence between  the  lines  of  true  and  apparent  level,  is  8 
inches  at  the  distance  of  a  mile  ;  but  since  it  varies  as  the 
square  of  the  distance,  it  is  very  insignificant  in  sights  of 
ordinary  length,  (one-eighth  of  an  inch  for  a  sight  of  one- 
eighth  of  a  mile)  and  may  be  completely  compensated  by 
setting  the  instrument  midway  between  the  points  whose 
difference  of  level  is  desired  ;  a  precaution  which  should 
always  be  taken,  when  possible.  If  the  ground  renders 
sights  of  unequal  length  unavoidable,  a  balance  should  be 
struck  as  soon  as  possible,  by  adopting  corresponding 
inequalities  in  the  contrary  direction. 

The  heights  observed  along  the  length  of  the  road,  which 
give  its  "  longitudinal  section,"  should  be  taken '  at  every 
change  of  slope  ;  and  at  every  hundred  feet,  when  the  line 
is  finally  located. 

It  is  also  necessary  to  take  them  at  right  angles  to  its 
length,  in  order  to  obtain  the  "  transverse"  or  "  cross  sec- 
tions.'1'' These  are  required  for  the  subsequent  calcula- 
tions of  the  "  cutting  and  filling,"  and  to  enable  the  engi- 
neer to  see  what  would  Fig  44  • 
be  the  effect  upon  these, 
of  moving  the  line  to  the 
right  or  to  the  left.  The 
right  page  of  the  note- 
book  is  usually  devoted;  ^~ 

*  For  another  form  of  Levelling:  Field-book,  see  page  145 ». 


100  THE  LOCATION  OF  ROADS. 

in  part,  to  the  cross-sections,  taken  in  reference  to  any 
station,  as  B.  In  this  example,  on  the  right,  the  ground 
rises  10  feet  in  going  out  30  ;  on  the  left,  it  falls  20  in  a 
"  distance  out"  of  50. 

These  cross-sections  should  be  taken  at  every  change 
of  longitudinal  slope.  At  every  change  of  slope  trans- 
versely, single  heights  and  "distances  out"  should  be 
taken.  The  future  calculations  of  cubical  contents  will 
be  facilitated  by  observing  the  following  rules  : — 

1.  Take  a  cross-section  whenever  either  edge  of  the 
road  passes   from    excavation   to    embankment,   or  vice 
versa. 

2.  When  the  road  is  partly  in  excavation  and  partly  in 
embankment,  ascertain  the  "  distance  out"  at  which  the 
grade,  or  level  of  the  base,  cuts  the  surface  of  the  ground. 

3*  Take  heights  at  each  edge  of  the  base,  i.  e.  at  dis- 
tances on  each  side  of  the  centre  line,  equal  to  the  half 
width  of  the  base  of  the  road. 

4.  Take  the  intermediate  cross-sections  at  some  deci- 
mal division  of  100  feet. 

The  Mountain  Barometer  is  an  instrument  of  great  value 
for  the  rapid  determination,  with  approximate  accuracy,  of  the 
heights  of  the  leading  points  in  an  extensive  district  of  country.* 

The  temperature  of  boiling  water  supplies  another  easy 
means  of  approximation.  The  degree  of  heat  at  which  water 
boils  diminishing  as  the  height  increases,  tables  have  been 
constructed  from  observation,  with  the  aid  of  which  the  height 
of  a  place  may  be  calculated  from  the  temperature  at  which 
water  there  boils,  j 


*  Gillespie's  Levelling,  p.  79. 

t  See  Silliman's  Journal,  1846,  pp.  134-«. 


MAPPING    THE    SURVEY.  101 


4.    MAPPING    THE    SURVEY. 

The  lengths,  directions,  and  heights  of  the  different 
portions  of  the  line  having  been  ascertained,  they  are  next 
to  be  represented  on  paper,  in  such  a  way  as  to  convey  to 
an  instructed  eye  a  complete  idea  of  the  ground  over  which 
the  route  passes.  This  idea  will  be  as  accurate  as  could  be 
obtained  from  actual  examination,  and  much  more  easily 
embraced  by  the  mind  ;  the  details  being  made  subordinate 
to  the  leading  features. 

The  mapping  of  a  line  comprehends  two  distinct 
branches  : 

1.  The  plot. 

2.  The  profile. 

THE    PLOT    OF  A   LINE. 

This  represents  the  lengths  and  directions  of  the  differ- 
ent portions  of  a  line,  projected  on  a  horizontal  plane,  as 
they  would  be  seen  by  an  eye  looking  down  upon  them 
from  a  great  height  directly  above  them.  If  the  lengths 
have  been  measured  horizontally,  as  is  usual,  they  will 
require  no  farther  reduction.  Before  commencing  the 
plot,  its  "  scale"  must  be  determined,  i.  e.,  what  propor- 
tion the  representation  is  to  bear  to  the  reality,  or  how 
many  feet  of  the  line  each  foot  of  the  plot  is  to  represent. 
If  one  foot  of  the  plot  represent  1000  feet  of  the  line,  100 
feet  of  the  latter  will  occupy  one  tenth  of  a  foot  on  the 
plot,  and  so  on.  Any  convenient  scale  may  be  assumed, 
but  must  be  carefully  preserved  unchanged  in  the  same 
plot.  The  changes  in  the  direction  of  the  line,  or  the 
angles  of  deflection  of  its  adjacent  parts,  may  be  most 
easily  laid  down,  as  explained  on  page  91,  by  describing 
an  arc  from  the  angular  point  with  the  same  radius  used 


102 


THE    LOCATION    OF   ROADS. 


on  the  ground,  (taken  to  the  proper  scale)  and  setting  off 
on  the  arc,  as  a  chord  the  proper  distance  measured  in 
like  manner. 

If  the  deflection  had  been  measured  by  an  angular  in- 
strument, (which,  however,  the  preceding  method  dis- 
penses with)  it  would  have  been  laid  down  on  the  paper 
by  a  "  protractor,"  the  most  usual  form  of  which  is  a 
small  brass  semicircle,  divided  into  degrees  similar  to 
those  on  the  instrument. 

Upon  the  plot,  it  is  usual  to  represent  the  hills  and  val- 
leys in  the  vicinity  of  the  line  ;  but  since  they  are  supposed 
lo  be  seen  horizontally  projected  in  a  "  map-view,"  as  they 
would  appear  to  an  eye  looking  down  upon  them  from  an 
infinite  height,  they  cannot  be  drawn  with  the  rises  and  falls 
of  the  front  view  in  which  we  usually  see  them,  but  must 
be  represented  by  some  artificial  and  conventional  method. 
They  are  accordingly  supposed  to  be  cut  by  a  number  of 
equidistant  horizontal  planes,  and  the  horizontal  "  contour 
curves"  of  intersection  to  be  drawn  upon  the  map,  the  in- 
tervals between  them  being  filled  up  by  short  hatchings 
perpendicular  to  the  curves.*  Hills,  represented  on  these 
principles,  are  indicated  by  numerous  diverging  lines, 
shorter,  nearer,  and  heavier,  in  proportion  as  the  hill  is 
Pteeper,  and  vice  versa.  See  the  examples  on  pages  83-4. 

All  water-courses  must  also  be  carefully  represented  on 
the  plot ;  and  the  nature  of  the  surface,  whether  pasture, 
ploughed  land,  swamp,  woods,  &c.,  together  with  the  de- 
tached objects  upon  it,  such  as  houses,  mills,  churches, 
&c.,  be  indicated  by  certain  arbitrary  signs.  For  our 
purposes  they  are  not  necessary,  but  may  be  found,  if 
desired,  in  any  topographical  manual. 

*  For  fuller  details,  eee  Gillespie'e  "Levelling,  Topography,  and  Elghej 
Surveying,"  Part  TV. 


THE    PROFILE    OF    A    LINE.  108 


THE    PROFILE    OF    A    LINE. 

This  represents,  to  any  desired  scale,  the  heights  and 
distances  of  the  various  points  of  a  line,  projected  on  a 
vertical  plane.  It  thus  gives  a  "  side-view"  of  its  ascents 
and  descents.  Any  point  on  the  paper  being  assumed  for 
the  first  station,  a  horizontal  line  is  drawn  through  it ;  the 
distance  to  the  next  station  is  measured  along  it  to  the 
required  scale  ;  at  the  termination  of  this  distance  a  verti- 
cal line  is  drawn  ;  and  the  given  height  of  the  second  sta- 
tion above  or  below  the  first  is  set  off  on  this  vertical  line. 
The  point  thus  fixed  determines  the  second  station,  and  a 
line  joining  it  to  the  first  station  represents  the  slope  of 
the  ground  between  the  two.  The  process  is  repeated 
for  the  next  station,  &c. 

But  the  rises  and  falls  of  a  line  are  always  very  small 
in  proportion  to  the  distances  passed  over ;  even  moun- 
tains being  merely  as  the  roughnesses  of  the  rind  of  an 
orange.  If  the  distances  and  the  heights  were  represent- 
ed on  a  profile  to  the  same  scale,  the  latter  would  be 
hardly  visible.  To  make  them  more  apparent  it  is  usual 
to  "  exaggerate  the  vertical  scale"  tenfold,  or  more,  i.  e., 
to  make  the  representation  of  a  foot  of  height  ten  times  as 
great  as  that  of  a  foot  of  length.  Take,  for  instance,  the 
example  on  page  98.  Let  one  inch  represent  one  hun- 
dred feet  for  the  distances,  and  ten  feet  for  the  heights. 

From  A  draw  a  horizontal  line.  Measure  on  it  one 
inch,  representing  one  hundred  feet  of  length.  Thence 
draw  downwards  a  vertical  line.  Measure  on  it  four-tenths 
of  an  inch,  representing  four  feet  of  height.  This  fixes  the 
point  B.  Join  A  to  B.  This  line  AB  represents  the 
slope  of  the  ground.  Next,  along  the  horizontal  line, 
measure  six-tenths  of  an  inch  farther,  representing  sixty  feet 


104  THE    LOCATION    OF   ROADS. 

Fig.  45. 


100  eo  ;     -*o      E       70 


of  length.  Measure  on  a  vertical  line  thence  drawn,  five- 
tenths  of  an  inch,  representing  five  feet  of  height.  This 
fixes  C.  Join  C  to  B.  Proceed  in  like  manner  for  all 
the  levels. 

The  distances  may  be  written  horizontally  in  their  ap- 
propriate places,  and  the  heights  or  depths  of  the  ground 
(above  or  below  the  datum  line)  vertically,  along  the 
lines  which  represent  them,  as  in  the  figure. 

5.   ESTABLISHING  THE   GEADES. 

The  grade  of  a  line  is  its  longitudinal  slope,  and  is 
designated  by  the  ratio  between  its  length  and  the  dif- 
ference of  height  of  its  two  extremities.  The  ratio  of 
these  two  quantities  gives  it  its  name,  as  we  have  seen ; 
the  road  being  said  to  have  a  grade  of  one  in  thirty  when 
it  rises  or  falls  one  foot  in  each  thirty  feet  of  length. 
When  the  "profile"  of  a. proposed  route  has  been  made, 
a  "grade-line"  is  drawn  upon  it  (usually  in  red)  in  such 
a  manner  as  to  follow  its  general  slope,  but  to  average  its 
Fig.  46. 


4000 


irregular  elevations  and  depressions,  as  in  the  figure.    The 
ratio  between  the  whole  distance  and  the  height  is  then  to 


ESTABLISHING  THE  GRADES.  105 

be  calculated.  If,  as  in  the  figure,  it  rise  100  in  4000,  the 
grade  is  one  in  forty,  flatter  than  our  assumed  limit  of  one 
in  thirty,  and  the  line  will  be  a  satisfactory  one,  if  on  cal- 
culation it  be  found  that  the  cuttings  about  equal  the  fill- 
ings. If  either  be  much  in  excess,  the  grade  is  altered  to 
equalize  them,  as  will  be  explained  under  the  next  head. 
But  if  the  grade  be  found  steeper  than  the  limit,  as  when 
it  ascends-  the  face  of  a  hill  with  a  rise  of  100  feet  in 
1500,  or  a  slope  of  one  in  fifteen,  either  the  hill  must  be 
cut  down,  or,  which  is  generally  preferable,  the  length  of 
the  line  must  be  increased  so  as  to  equal  100  x  30  =  3000. 
The  best  method  of  obtaining  this  increased  length,  or 
"development,"  (whether  by  a  zigzag  or  by  a  single 
oblique  line)  will  depend  upon  the  manner  in  which  the 
line  meets  the  face  of  the  hill,  whether  at  right  angles  01 
obliquely,  and  should  be  determined  by  geometric  con- 
structions upon  the  plot,  such  as  those  which  follow 
modified  if  necessary  by  the  features  of  the  ground. 

Problem.   To  fix  the  position  of  a  line  joining  two  giver. 

points,  so  that  it  shall  ascend  with  a  given  grade  a  slope 

steeper  than  this  grade,  and  shall  also  be  the  shortest  possible 

line  which  will  fulfil  this  condition.* 

Case  1.  When  the  straight  line  joining  the  two  points  meets 

the  slope  at  right  angles. 

Fig.  47. 


Gay  flier,  p.  13 


106  THE  LOCATION  OF  ROADS. 

Let  A  and  B  be  the  given  points,  and  let  the  top  and  bottom 
lines  of  the  slope  to  be  ascended  be  considered  parallel.  Let 
mn  represent  the  length  which  the  road  up  the  hill  must  have 
to  ascend  with  the  proper  grade.  Join  the  given  points  by  a 
straight  line,  and  between  the  points  C  and  D,  at  which  this 
line  meets  the  top  and  bottom  line,  establish  a  zigzag,  of  a 
sufficient  number  of  turns  to  make  its  entire  length  equal  to 
mn,  the  **  development"  required  ;  which  in  the  instance  last 
supposed  would  be  3000  feet,  the  straight  line  CD  being  only 
1500.  / 

The  road  which  ascends  the  Catskill  mountain  makes  seven 
such  zigzags  or  tacks.  Their  angles  should  be  rounded  off  by 
curves,  as  explained  in  a  following  article  on  "  Final  Location." 
At  these  curves  the  width  of  the  road  should  be  increased,  as 
directed  on  page  46. 

Case  2.  When  the  straight  line  meets  the  slope  obliquely, 
and  the  two  given  points  are  very  distant  from  each  other. 

Fig.  48. 


Let  A  and  B  be  the  given  points.  Between  the  top  and 
bottom  lines  of  the  slope  draw  a  line  mn  at  such  a  degree  of 
obliquity  as  will  make  its  length  equal  to  the  development  re- 
quired, which,  in  the  instance  supposed,  is  3000  feet.  The 
straight  line  AB  would  be  too  steep  between  C  and  E.  There- 
fore from  the  point  C  draw  a  line  CD,  parallel  and  therefore 
equal  to  mn  Join  DB,  and  the  line  ACDB  will  be  the  one 
desired. 


ESTABLISHING  THE  GRADES.  107 

A  zigzag  between  C  and  E  would  give  a  longer  line ;  for, 
comparing  the  parts  of  the  line  thus  obtained  with  those  of  the 
other,  we  find  AC  common  to  both ;  the  zigzag  CE  equal  to 
CD  by  construction  ;  and  EB  longer  than  DB,  because  farther 
from  the  perpendicular. 

The  construction  above  directed  is  merely  approximately 
true,  becoming  perfectly  so  only  when  the  points  A  and  B  are 
infinitely  distant  from  each  other.  The  strict  construction  is 
that  which  follows. 

Case3.  When  the  straight  line  meets  the  slope  obliquely,  and 
the  two  given  points  are  near  each  other. 

From  the  given  points  A  and  B  draw  perpendiculars  to  the 
nearest  edges  of  the  slope.  The  line  joining  the  feet  of  these 
perpendiculars  will  be  less  than,  equal  to,  or  greater  than,  the 
developed  line  mn,  according  to  the  steepness  of  the  slope, 
and  the  degree  of  obliquity  with  which  it  is  met  by  the  straight 
line  which  joins  the  given  points.  Three  sub-cases,  requiring 
different  constructions,  are  thus  formed. 

Sub-case  1.  When  the  line  joining  the  perpendiculars  is 
shorter  than  the  developed  line  mn. 

Fig.  49 


From  A  and  B  draw  AC  and  BD  perpendicular  to  the  edges 
of  the  slope.  Join  C  and  D  by  a  zigzag  line,  equal  in  length 
to  the  developed  line  mn.  Then  will  the  line  thus  obtaiaed 


108  THE     LOCATION    OF    ROADS. 

fulfil  the  conditions  required  ;  the  length  of  the  zigzag  being 
equal  to  the  necessary  length  mn,  and  the  lines  AC  and  BE 
being  perpendicular  to  the  top  and  bottom  of  the  hill,  and  there- 
fore the  shortest  possible  distances  to  it. 

Sub-case  2.  When  the  line  joining  the  perpendiculars  it 
equal  to  the  developed  line  mn. 

Fig.  50. 


Draw  the  perpendiculars  AC  and  BD,  as  before,  and  join 
their  feet  by  the  line  CD.  Then  will  the  line  ACDB  be 
shorter  than  any  other  line,  (as  AC'D'B,  obtained  by  the  con- 
struction of  Case  2)  for  AC  and  BD,  being  perpendiculars,  are 
the  shortest  possible,  and  CD  has  a  constant  length,  wherever 
it  may  be  placed. 

A  zigzag  line  from  C' to  E  would  not  produce  the  shortest 
line,  for  the  same  reasons  as  in  Case  2. 

Sub-case  3.  When  the  line  joining  the  perpendiculars  is 
longer  than  the  developed  line  mn. 

From  A,  Fig.  51,  draw  AE  parallel  and  equal  to  mn.  Join  EB. 
From  the  point  D  (where  this  line  intersects  the  edge  of  the 
slope)  draw  DC  parallel  and  equal  to  AE.  Join  CA.  Then 
will  ACDB  be  the  shortest  line  required. 

For,  AE,  being  equal  to  mn,  cannot  be  shortened,  and  EB 
is  a  straight  line,  and  therefore  the  shortest  possible  line,  as  is 


ESTABLISHING    THE    GRADES, 
Fig.  51. 


109 


consequently  the  whole  line  AEDB.  But  this  line  is  in  the 
wrong  place,  and  its  parts  require  to  be  transported  parallel  to 
themselves.  By  this  operation  is  formed  the  line  ACDB, 
which  has  all  its  parts  equal  to  those  of  the  former  line,  and 
which  is  therefore  the  shortest  possible. 

It  might  seem  preferable  to  adopt  the  direct  line  AB,  and  to 
ascend  the  hill  by  a  zigzag  from  F  to  G  ;  but  this  would  not 
give  the  shortest  line  ;  for  AF  and  GB  are  longer  respectively 
than  AC  and  DB,  because  farther  from  the  perpendiculars. 

When  the  lines  AC  and  DB,  obtained  by  the  construction 
above  directed,  fall  beyond  the  perpendiculars  let  fall  from  A 
and  B  upon  the  top  and  bottom  of  the  slope,  this  result  shows 
that  this  construction  is  inapplicable,  and  that  the  case  is  one 
in  which  it  is  proper  to  adopt  the  perpendiculars,  and  to  join 
them  by  a  zigzag  of  the  proper  length. 

Case  4.  When  two  neighboring  slopes  are  separated  by  a 
level  space ;  whether  a  valley,  or  a  table-land  on  the  ridge  of 
a  hill. 

Between  the  top  and  bottom  lines  of  one  slope  draw  the  line 
mn,  equal  in  length  to  the  developed  line  with  which  that  slope 
must  be  crossed  ;  and  in  like  manner  on  the  second  slope,  draw 
the  line  pq. 

Then  from  A  draw  AE,  parallel  and  equal  to  mn.  From  E 
draw  EF  parallel  and  equal  to  pq.  Join  FB.  The  line  AEFB 


no 


THE    LOCATION    OF   ROADS. 
Fig.  52. 


is  the  shortest  line  possible,  for  the  same  reasons  as  was  AEB 
in  the  preceding  sub-case  3.  But  its  parts  require  to  be  differ- 
ently arranged  without  changing  their  length,  which  is  effected 
thus.  From  H  draw  HG  parallel  and  equal  to  FE.  From  G 
draw  GD  parallel  to  HF,  and  terminating  at  the  edge  of  the 
next  slope.  From  D  draw  DC  parallel  and  equal  to  EA.  Join 
CA  by  a  line  which  will  be  parallel  to  FH.  This  new  line 
ACDGHB  is  equal  to  the  former  line  AEFB,  and  therefore  is 
the  shortest  line  required. 

If  the  space  between  the  two  slopes  was  a  valley,  in  which 
there  was  a  given  point  to  be  passed  through,  as  a  bridge,  the 
problem  would  divide  itself  into  two  others,  such  ,s  have  been 
solved  in  the  preceding  cases. 

Grades  may  be  approximately  estimated  upon  the 
ground,  (without  measuring  distances  and  heights)  by  a 
slight  addition  to  the  "plumb-line  level,"  described  on  page 
93.  Connect  the  horizontal  and  vertical  bars  by  oblique 
braces.  To  prepare  it  for  use,  depress  or  elevate  the 
sights,  sc  that  their  line  coincides  with  an  ascent  or  de 


MEASLUING    GRADES. 


Ill 


scent  of  one  in  thirty,  or  any  other  grade  previously  estab 
lished  by  levelling.  Mark  the  point  at  which  the  plumb- 
line  now  cuts  the  oblique  braces.  Do  the  same  for  other 
grades,  the  more  varied  the  better,  and  the  instrument 
will  thus  become  a  clinometer,  or  grade-measurer.  When 
it  is  placed  upon  any  slope,  and  its  sights  directed  to  any 
object  (such  as  a  target  on  a  rod,  or  a  paper  in  a  cleft 
stu  k)  at  the  same  height  above  the  surface  as  its  upper 
edge,  that  division  on  the  brace  which  is  cut  by  the  plumb- 
line  will  indicate  the  inclination  of  the  slope.  The  A  level 
described  on  page  94,  may  be  used  in  a  similar  manner,  a 
scale  having  been  in  the  same  way  formed  on  the  bar  DE. 
An  extempore  clinometer  may  be  made  with  a  sheet  of 
paper,  a  thread,  and  a  pebble.  Fig.  53. 

Take  a  sheet  of  paper  of  any 
shape,  double  it,  and  a  straight 
line  is  formed;  double  it  again 
along  the  straight  line,  and 
four  right  angles  are  obtained. 
Cut  out  one  of  the  right  an- 
gles, and  double  it  so  as  to 
bring  the  sides  of  the  right 
angle  together,  and  it  will  be 
bisected,  forming  two  angles  of 
45°.  Fold  this  in  three  equal  parts,  jnd  angles  of  15° 
will  be  formed  ;  repeat  the  last  operations,  and  angles  of 
5°  will  be  obtained.  The  subdivision  may  be  carried  as 
far  as  desired.  To  use  the  instrument,  form  a  plumb-line 
by  tying  a  pebble  to  the  end  of  a  thread,  and  attach  it  at 
the  centre  of  the  angles.  Holding  the  right  angle  to  the 
eye,  if  the  grade  be  descending,  or  the  opposite  corner  if 
it  be  ascending,  turn  the  paper  till  its  edge  is  in  the  line 
which  passes  from  the  eye  to  some  object  at  the  same 


112  THE  LOCATION  OF  ROADS. 

height  above  the  surface.  The  plumb-line  will  then  indi- 
cate the  angle  of  the  slope.  In  the  figure  it  strikes  5°. 
equivalent,  by  the  table  on  page  44,  to  1  in  1 1 . 


6.    CALCULATING  EXCAVATION  AND  EMBANKMENT 

The  proper  grade-line  having  been  thus  determined, 
and  drawn  on  the  profile,  (which  shows  the  heights  of  the 
ground  over  which  the  line  passes)  the  difference  between 
the  height  of  the  ground  and  that  of  the  grade-line  at  any 
point,  will  of  course  represent  the  depth  of  cutting,  (or  ex- 
cavation) or  the  height  of  filling  (or  embankment)  as  the 
case  may  be,  at  that  point.  This  depth,  or  height,  ir, 
feet  and  decimal  parts  of  a  foot,  should  be  written  in  red 
figures  (cotes  rouges)  at  the  proper  points  of  the  profile. 
With  these,  knowing  also  the  intended  width  of  the  road 
and  the  inclination  of  the  side-slopes,  the  cubical  contents 
of  the  excavations  and  embankments,  or  the  amount  of 
"  earth-work,"  may  be  accurately  calculated. 

The  cost  of  the  road  will  depend  in  a  great  degree 
upon  the  quantity  of  the  "  earth-work"  to  be  done,  and 
may  be  greatly  lessened  by  making  the  amount  of  exca- 
vation precisely  equal  to  that  of  embankment,  so  that 
what  is  dug  out  of  the  hills  may  just  suffice  to  fill  up  the 
hollows.  It  is  therefore  very  important  for  economy  to 
calculate  these  amounts  with  accuracy  before  the  final 
location  of  the  line,  so  that  if  they  are  found  to  be  unequal, 
the  position  and  grades  of  the  line  may  be  changed  to 
produce  the  equality  desired. 

This  accurate  calculation  is  necessary,  after  the  final 
location,  for  another  reason  ;  inasmuch  as  the  contractors, 
who  usually  perform  the  work,  are  paid,  not  by  the  day, 
nor  in  the  lump,  but  by  a  certain  price  per  cubic  yard,  the 


EXCAVATION  AND  EMBANKMENT.  1  I  3 

exact  determination  of  the  number  of  which  is  therefore 
required  to  ascertain  their  just  dues. 

PRELIMINARY  ARRANGEMENTS. 

For  calculating  the  cubical  contents  of  the  solid  mass 
of  earth  cut  out  or  filled  in,  four  different  methods  are  in 
common  use.  All  four,  however,  require  the  same  pre- 
liminary arrangements  and  preparations,  which  will  there- 
fore be  now  given. 

Figure  54  is  a  plan  (on  a  scale  of  800  feet  to  the  inch) 
and  figure  55  a  profile  (on  a  vertical  scale  of  80  feel  to 
the  inch)  of  an  old  line  of  road,  which  it  is  desired  to  im- 
prove by  cutting  down  the  hill  and  filling  up  the  hollow, 
so  as  to  form  a  single  slope,  with  a  uniform  grade,  from 
A  to  B.*  The  distances  between  the  stations  are  written 
horizontally ;  the  heights  of  the  ground  above  the  datum 
line  are  written  along  the  vertical  lines  which  represent 
them ;  and  at  the  extremities  of  these  vertical  lines  are 
placed  the  numbers  which  represent  the  depths  of  cutting 
or  filling  at  those  points,  and  which  are  equal  to  the  dif- 
ferences between  the  heights  of  the  ground  and  of  the 
"  grade-line,"  or  new  road 

SECTIO-PLANOGRAPHY. 

A  method  of  representing  the  cuttings  and  fillings  upon 
the  plan, devised  by  Sir  John  Macneill,  has  been  named 
'  Sectio-planography  ."  Usually  the  plan  and  the  profile 
are  drawn  separately,  and  when  the  former  varies  much 
from  a  straight  line,  it  is  difficult  for  an  unpractised 


*  S'naan  TO  Levelling,  Am.  edition,  p.  81 
8 


14 


THE    LOCATION    OF    ROADS. 
Fig.  54. 


i+18. 


+20. 


-s. 


EXC  iVATION  AND  EMBANKMENT. 

eye  to  discover  the  corresponding  points 
of  the  plan  and  profile  ;  as  the  latter 
is  fowned  by  placing  all  the  distances 
along  a  straight  base  line,  and  therefore 
fills  a  longer  space  than  the  winding  plan  ; 
and  as  the  two  are  also  frequently  drawn 
far  apart,  or  even  on  different  sheets. 
In  the  improved  method,  the  depths  of 
cutting  and  of  filling  at  each  station  are 
set  off  on  one  side  or  the  other  of  the 
plan  of  the  line,  as  laid  down  upon  the 
map,  so  that  all  the  information  desired, 
with  regard  to  any  portion  of  the  line, 
may  be  found  on  that  very  spot.  The 
accompanying  figure  shows  its  applica- 
tion to  the  preceding  example,  the  "  plan" 
of  which  has  been  intentionally  made 
very  winding. 

To  make  the  distinction  more  striking, 
the  cuttings  may  be  shaded  with  lines' 
perpendicular  to  the  line  of  the  road,  and 
the  fillings  with  lines  parallel  to  it ;  or 
the  former  may  be  colored  red,  and  the 
latter  blue.* 


115 


Fig.  56 


TABULAR    ENTRIES. 

The  data  of  the  profile,  with  those 
deduced  therefrom,  should  be  presented 
in  a  tabular  form,  such  as  that  which  fol- 
lows, and  which  refers  to  figure  55. 

*  See  Simms  on  Sectio-Planography. 


116 


THE  LOCATION   OF  ROADS. 


1 

2 

3 

4 

5 

6 

7 

Station. 

Distances. 

Height  of  ground 
above  datum  line. 

Rise  or  fall 
of  the  grade  line 
for  each  distance. 

Height  of 
grade 
above  datum. 

f 

Fill. 

1 

46.0 

46.0 

0 

2 

561 

59.2 

—  4.8 

41.2 

18. 

3 

858 

53.9 

—  7.3 

33.9 

20. 

4 

825 

26.9 

—  7.0 

26.9 

0 

0 

5 

820 

0.9 

—  7.0 

19.9 

19. 

6 

825 

4.9 

—  7.0 

12.9 

8. 

7. 

330 

10.0 

—  2.9 

10.9 

0 

4219 

36.0 

1 

The  first  column  contains  the  nuiiioer  of  the  station,  01 
point,  the  height  of  which  above  the  datum  line  is  con- 
tained in  the  third  column.  The  second  column  records 
the  distances  between  the  stations. 

The  fourth  column  shows  the  rise  or  fall  of  grade  for 
each  distance,  obtained  by  a  simple  proportion,  the  whole 
distance  and  difference  of  height  being  known.  Thus, 
4219:  5.61  :  :  36  :  4.8. 

The  fifth  column  shows  the  height  of  the  grade  line, 
i.  e.  of  the  road  as  improved,  above  the  datum  line  at  each 
station.  The  numbers  in  it  are  obtained  by  subtracting 
successively  the  fall  between  two  stations,  as  recorded  in 
the  fourth  column,  from  the  height  of  the  grade  line  at  the 
preceding  station.  Thus,  46  —  4.8  =  41.2. 

The  sixth  and  seventh  columns  show  the  depths  of  cut- 
ting or  filling  at  any  station.  They  are _ the  differences 
between  the  height  (from  column  3)  of  the  ground  at  any 
station,  and  the  height  of  the  grade-line  (from  column  5) 
for  the  same  station. 

The  station  (No.  4)  at  which  the  cutting  ends,  ar.d  the 
filling  begins,  is  called  a  "  Point  of  Passage." 


CUBICAL  CONTENTS.  117 

CUBICAL  CONTENTS. 

With  these  data  the  calculation  may  be  commenced, 
and  the  end  areas — or  middle  areas,  or  both,  according 
to  the  method  adopted — be  sought,  and  the  cubical  con- 
tents thence  deduced.  The  details  of  thes"e  calculations 
are  of  great  importance  to  the  practical  engineer,  but  oc- 
cupy so  much  space,  that  they  have  been  transferred  to 
the  Appendix.  The  following  are  their  results. 

"  Averaging  end  areas"  is  the  most  usual  method  of 
calculation  in  this  country,  but  gives  a  result  which  al- 
ways exceeds  the  correct  amount,  in  a  greater  or  less  de 
gree,  according  to  the  inequality  of  the  end  areas.  In  the 
present  example,  its  error  in  excess  is  10,000  cubic  yards, 
which  amount,  beyond  what  was  justly  due  for  the  work 
done,  would  be  paid  by  a  company  or  town  by  which 
this  improvement  should  be  made,  if  their  engineers 
should  adopt  this  method  of  calculation. 

The  calculation  by  "  Middle  areas"  gives  an  amount 
which  falls  short  of  the  true  one,  by  a  deficiency  equal  to 
exactly  half  of  the  excess  of  the  preceding  method. 

"  The  Prismoidal  formula"  alone  gives  the  correct 
amount ;  which,  in  this  example,  is  2,200,968  cubic  feet 
of  excavation,  and  1,541,152  of  embankment. 

The  fourth  method,  by  "  Mean  Proportionals"  gives 
a  result  always  less  than  the  true  one,  and  exceedingly 
erroneous  when  one  of  the  end  areas  is  nothing. 

The  substitution  of  the  correct  Prismoidal  method  for 
(he  erroneous  ones  which  are  so  frequently  employed,  is 
demanded  by  every  consideration  of  accuracy,  economy, 
honesty,  and  justice  ;  and  the  full  calculations  in  the  Ap- 
pendix show  that  the  additional  labor  required  is  too  tri« 
fling  to  be  a  reasonable  obstacle. 


118  THE     LOCATION    OF    ROADS 

BALANCING    THE    EXCAVATION    AND    EMBANKMENT. 

When  the  quantity  of  excavation  on  any  given  portion 
of  the  road  exceeds  that  of  the  embankment,  the  excess 
is  called  "  Surplus,"  and  must  be  deposited,  upon  the 
adjoining  land;  in  masses  called  "  Spoil-banks" 

When  the  excavation  is  insufficient  to  make  the  em 
bankment,  the  deficiency  is  called  "Wantage,"  and  musl 
be  supplied  from  extra  "  Side-cuttings"  in  the  neighbor 
ing  fields. 

Both  these  cases  are  expensive  and  otherwise  objection 
able  ;  it  is  therefore  very  desirable  to  make  the  excavation 
and  embankment  "  balance"  each  other,  so  that  the  earth 
dug  out  may  just  suffice  to  fill  up  the  hollows.  If  the 
calculations  show  much  disparity  in  the  two  amounts,  the 
location  of  the  line  must  be  changed  in  some  way,  so  as 
to  effect  the  desired  equality. 

This  equalization  must,  however,  be  restrained  within 
certain  limits  ;  for  it  should  evidently  be  abandoned,  when, 
in  order  to  find  sufficient  excavation  to  make  the  embank 
ment,  it  would  be  necessary  to  go  to  such  a  distance  that 
the  cost  of  transport  would  exceed  the  cost  of  making 
side-cuttings  for  the  embankment,  and  of  depositing  the 
distant  excavation  in  spoil-banks.  The  comparison  ot 
the  price  of  transport  with  that  of  excavation  and  of  land, 
will  therefore  determine  the  distance  within  which  the 
balancing  mrst  be  established. 

SHRINKAGE. 

The  equality  recommended  must  be  taken  with  an  im 
portant  qualification,  dependent  on  the  fact  that  earth 
transferred  from  excavation  to  embankment  shrinks,  or  is 
compressed,  so  as  to  occupy,  on  the  average,  one-tenth 


SHRINKAGE  119 

less  space  in  bank  lhan  it  did  in  its  natural  state,  100  cu- 
bic yards  "  shrinking"  into  90. 

Rock,  on  the  contrary,  occupies  more  space  when  bro- 
ken, its  bulk  increasing  by  about  one-half. 

In  experiments  made  on  a  large  scale,  by  Ellwood 
Morris,  C.  E.,*  the  shrinkage  of  light  sandy  earth  was 
|  of  its  volume  in  excavation  ;  of  yellow  clayey  earth 
TV ;  and  of  gravelly  earth  TV-  The  increase  of  hard 
sandstone  rock,  quarried  in  large  fragments,  was  T\  of  its 
volume  in  excavation  ;  and  of  blue  slate-rock,  broken  into 
small  fragments,  T\. 

Upon  some  of  the  public  works  of  the  state  of  New 
York,  the  usual  allowance  has  been  for  the  shrinkage  of 
gravel  and  sand  8  percent.;  for  clay  10  per  cent.;  for 
loam  12  per  cent.  ;  for  mucking,  or  surface  soil,  15  per 
cent. ;  and  for  clay  "  puddled"  25  per  cent.  The  in- 
crease of  bulk  of  rock  was  taken  at  one-third,  or  some- 
limes  at  one-half;  though  some  experiments  showed  that 
one  yard  of  slate-rock  made  from  1.75  to  1.8  cubic  yards 
of  embankment. 

These  considerations  lead  us  to  modify  the  require- 
ments of  equality  in  the  excavations  and  embankments, 
and  to  adjust  them  so  that  the  former  shall  exceed  the  lat- 
ter by  about  10  per  cent. 

CHANGE    OF    GRADE. 

We  will  now  take  up  the  example  on  page  114,  in 
which  we  find  the  excess  of  the  excavation  over  the  em- 
bankment, or  its  "  surplus,"  (according  to  the  correct  cal- 
culation, of  which  he  result  is  given,  on  page  117)  to  be 
659,816  cubic  feet.  We  must  therefore  change  the  grade, 

•  JoumaJ  of  the  Franklin  Institute,  October,  1841. 


IliO  THE    LOCATION    OF  ROADS. 

so  as  to  lessen  the  excavation,  and  increase  the  embank- 
ment, till  the  former  exceeds  the  latter  by  only  one-tenth  of 
itself.  The  grade  line  AB  (figure  55)  might  be  raised  either 
at  A  or  at  B.  The  latter  is  preferable,  since  it  will  increase 
the  gentleness  of  the  slope.  The  height  which  it  should 
be  raised  at  B  might  be  calculated  in  advance,  but  the 
complication  of  the  resulting  formula  is  so  great,  that  it 
will  be  better  to  assume  some  height,  (which  an  expe- 
rienced eye  can  do  with  considerable  accuracy)  and  hav- 
ing found,  by  a  simple  proportion,  the  changes  in  the  cut- 
tings and  fillings  at  each  station,  to  recalculate  the  whole 
cubic  contents.  If  the  desired  difference  has  not  been 
attained  in  the  result,  it  will  at  least  be  a  guide  by  which 
a  second  assumption  can  be  made  with  a  very  close  ap- 
proximation to  precision. 

Consider  the  grade  to  be  raised  three  feet  at  station  7.  A 
proportion  between  the  sum  of  the  distances  from  station  1  to 
7,  and  that  to  any  other  station,  will  give  the  change  of  cutting 
or  filling  at  that  station. 

For  station  2,  4219  :     561  :  :  3  :  0.4 

"       3,  4219  :  1419  :  :  3  :  1.0 

"        "       4,  4219  :  2244  :  :  3  :  1.6 

"        "       5,  4219  :  3064  :  :  3  :  2.2 

"       6,  4219  :  3889  :  :  3  :  2.8 

The  place  of  station  4,  i.  e.  the  "  Point  of  passage,"  is 
changed  by  the  elevation  of  the  grade  line  AB,  and  removed 
towards  station  3,  to  some  new  station  4' ;  see  Fig.  57.  A 
problem  here  presents  itself,  to  find  the  distance  between  the  old 
and  new  points  of  passage,  knowing  the  slope  of  the  grade  and 
that  of  the  ground.  Call  the  former  m  to  1,  and  the  latter 
n  to  1.  Let  the  elevation  of  the  new  grade  line  above  the  old 
point  of  passage  =  h  feet ;  and  the  distance  required  =  d. 

An  inspection  of  the  figure  shows  that  the  heights  of  the 
two  right-angled  triangles,  whose  bases  are  d,  are  respectively 


CHANGE    OF    GRADK 
Fig.  57. 


.121 


d         d  d       d 

—  and  — .     It  is  also  evident  that  -  = 1-  h  ;  whence  is  ob- 

n         m  n      m 

tained  the  general  formula, 

A      j,     mn 
a  =  n . 


42 1Q 

In  the  present  case  (see  table  on  page  1 16)  m  =  — — -  =  128 , 

ob  —  «> 

825 _  IPJLrU?!  _ 

-  53.9  —  26.9  -  =  1<6  X  128^31  ~ 

The    new   station  4'  is   therefore   distant   from  station  3, 
825  —  65  =  760  feet,  and  from  station  5,  820  +  65  =  885  feet. 
Adopting  these  new  distances,  and  changing  the  cuttings  and 
fillings  in  accordance  with  the  elevations  of  grade  obtained  by 
the  proportions  on  the  preceding  page,  they  will  stand  thus  : 


Station. 

Distance. 

Elevation 
of  grade. 

New  Cut. 

New  Fill. 

1 

0.0 

0 

2 

561 

0.4 

17.6 

3 

858 

1.0 

19.0 

4' 

760 

1.6 

0 

0 

5 

885 

2.2 

21.2 

6 

825 

2.8 

10.8 

7 

330 

3.0 

3.0 

The  calculations  being  repeated  with  these  data,  it  will  be 
found  that  the  excavation  will  amount  to  2,048,000  cubic  feet, 


12SL  THE    LOCATION    OF    ROADS. 

and  the  embankment  to  1,980,000  ;  an  apparent  surplus  of 
P8,000  cubic  feet;  but  since,  in  order  to  allow  for  the  shrink- 
age, th"re  should  be  an  excess  of  205,000,  it  appears  that  there 
is  really  a  Wantage,  and  that  the  grade  has  been  raised  too 
much  ;  so  that  an  elevation  of  only  2{  feet  at  B  would  probably 
produce  the  desired  balance. 

TRANSVERSE    BALANCING. 

When  the  road  lies  along  the  side  of  a  slope,  so  that  it 
is  partly  in  excavation  and  partly  in  embankment,  it  is  ne 


Fig.  58. 


cessary  so  to  place  its  centre  line,  that  these  two  parts  ol 
its  cross-section  may  balance.  When  the  ground  has  a 
uniform  slope,  the  desired  end  would  be  obtained  (if  the 
side  slopes  were  the  same  for  excavation  and  embank- 
ment, and  if  no  "  shrinkage"  existed)  by  locating  the  cen- 
tre line  of  the  road  on  the  surface  of  the  ground.  In  other 
cases,  as  when  the  side  of  the  excavation  slopes  1  to  1, 
and  that  of  the  embankment  2  to  1 ,  a  formula  to  determine 
'he  position  of  the  centre  line  of  the  road  may  be  readily 
established. 

If  earth  be  wanted  for  a  neighboring  embankment,  the 
amount  of  excavation  may  be  easily  increased  by  moving 
the  road  farther  into  the  hill,  with  the  additional  advantage 
of  lessening  its  liability  to  slip.  The  line  mav  be  thus 


TRANSVERSE    BALANCING.  123 

changed  on  the  map,  according  to  the  notes  of  cross- 
sections  in  the  level  book,  and  be  subsequently  moved,  by 
a  corresponding  quantity,  on  the  ground. 

When  the  slope  of  the  ground  is  very  steep,  the  trans- 
verse balancing  must  be  disregarded,  and  the  road  made 
chiefly  in  excavation,  to  avoid  the  insecurity  of  a  high 
embankment,  as  will  be  explained  under  "  Construction." 

DISTANCES    OF   TRANSPORT. 

The  equality  of  the  masses  of  excavation  and  embank 
ment  is  not  the  only  consideration.  The  distances  tc 
which  it  is  necessary  to  transport  the  earth  which  is 
moved,  must  also  be  taken  into  the  account.  Suppose 
that  a  mass  of  earth,  whose  surface  is  ABCD,  is  to  be 

Fig.  59 


DC  H  G 

removed  to  the  embankment  whose  surface  is  EFGH,  and 
which  has  a  thickness  sufficient  to  make  the  two  masses 
equal.  The  mean  distance  of  the  transport  is  required. 
Conceive  the  mass  ABCD  divided  into  a  very  great  num- 
ber of  smaller  masses.  The  sum  of  the  products  of  these 
portions,  by  the  distance  which  each  of  them  is  actually 
moved,  will  equal  the  product  of  the  sum  of  the  portions 
(i.  e.  of  the  whole  mass)  oy  the  mean  distance.  The 
mean  distance  therefore  equals  the  above  sum  of  products 
divided  by  the  whole  mass.* 

In  such  cases  as  usually  occur  on  a  road,  in  which  the 

*  Gayffier  p.  122. 


1^4  THE    LOCATION    OF    ROADS. 

cubes  of  excavation  and  embankment  are  comprised  be- 
tween two  parallel  planes,  whose  horizontal  traces  are 
ABEF  and  DCHG,  and  in  which  sections  made  by  other 
planes,  parallel  to  the  first,  cut  off  equal  partial  volumes,  we 
know,  from  the  principles  of  mechanics,  that  the  mean 
distance  desired  is  equal  to  the  distance  of  the  centres  of 
gravity  of  the  two  volumes.  In  the  simple  example  above, 
the  mean  distance  of  transport  would  be  the  distance  be- 
tween the  centres  of  the  two  rectangles. 

The  methods  of  apportioning  the  excavations  among 
different  embankments,  which  ought  to  be  adopted  in  more 
complicated  cases  of.  various  distances  of  transport,  in 
order  to  attain  the  minimum  of  labor  and  expense,  will  be 
considered  in  the  next  chapter,  which  treats  of  actual 
"  Construction." 


7.  ESTIMATE  OF  THE  COST  OF  A  ROAD. 

A  minute  and  careful  estimate  of  every  possible  source 
of  expense  in  the  construction  of  a  road,  is  a  very  impor- 
tant element  in  determining  its  location.  The  principal 
items  are  the  Earthwork,  Land,  Mechanical  structures. 
Engineering,  and  Contingencies. 

EARTHWORK. 

The  amount  of  "  Earths  «ik,"  or  excavation  and  em- 
bankment, is  supposed  to  have  been  determined  by  the 
preceding  calculations.  Its  cost  per  cubic  yard  depends 
on  the  wages  of  labor,  the  quality  of  the  earth,  and  the 
distance  over  which  it  is  moved. 

Wages.  The  daily  wages  of  an  ordinary  laboring  man 
vary  of  course  with  the  locality  and  the  season,  and  range 
from  50  cents  to  $1  25.  In  making  the  estimate,  it  must 


ESTIMATE    OF    COST.  1 5i5 

not  be  overlooked,  that  if  wages  are  at  that  time  unusually 
low,  they  will  be  likely  to  rise,  if  the  work  be  so  large 
in  amount  as  to  make  the  demand  for  labor  exceed  the 
supply. 

Quality.  The  amount  of  labor  required,  for  breaking 
up  and  removing  any  given  volume  of  earth,  will  of  course 
depend  upon  its  degree  of  compactness  and  cohesiveness, 
which  is  termed  its  "  quality."  This  is  estimated  by  the 
proportion  between  the  number  of  picks  in  use,  and  the 
number  of  shovels  which  these  picks  will  keep  constantly 
employed.  Thus,  if  the  earth  be  so  loose  that  it  can  be 
shovelled  up  without  being  loosened  by  the  pick,  it  is 
called  "earth  of  one  man."  If  it  be  so  hard  as  to  require 
one  picker,  or  "getter,"  to  be  constantly  employed,  to  keep 
one  shoveller,  or  "  filler,"  at  work,  it  is  called  "  earth  of 
two  men."  If  one  "  getter"  can  keep  two  "  fillers"  busy,  it 
is  "  earth  of  1  \  men  ;"  its  nomenclature  being  formed  by 
dividing  the  total  number  of  men  employed  by  the  number 
of  volumes  of  earth  removed.  The  "quality"  of  earth  can 
be  accurately  determined  only  by  actual  experiment,  though 
it  may  be  estimated  with  tolerable  precision  by  an  expe- 
rienced eye.  In  deep  cuts,  borings  should  be  made,  or 
shafts  sunk,  to  ascertain  the  nature  of  the  lower  strata. 
In  tjiis  examination  a  knowledge  of  the  geological  ar- 
rangement of  the  district  will  be  of  great  assistance. 

An  average  laborer  can  shovel  into  a  cart,  in  a  day  oi 
ten  hours,  from  10  to  14  cubic  yards,  measured  in  the 
embankment,  of  earth  previously  loosened  with  a  pick  or 
plough.  Of  hard  and  firm  gravelly  earth,  or  gravel  and 
clay  mixed,  he  can  load  10  cubic  yards  ;  of  loam,  (sand 
and  clay)  12  cubic  yards;  and  of  sandy  earth  14  cubic 
yards.*  To  loosen  the  earth  will  cost  from  1  to  8  cents 
«  Journal  of  Franklin  Institute,  September,  1841. 


J26 


THE    LOCATION    OF   ROADS. 


per  cubic  yard  ;  the  hardest  earth  requires  to  be  picked  ; 
the  others  may  be  ploughed ;  and  some  sandy  earth  does 
not  require  any  loosening,  but  may  be  shovelled  up  at 
once.  At  wages  of  one  dollar  per  day,  the  cost  of  shov- 
elling into  a  cart  would  therefore  be  from  7  to  10  cents 
per  cubic  yard ;  to  which  the  cost  of  loosening  must  be 
added.  If  it  were  "  earth  of  two  men,"  it  would  cost 
double.  The  excavation  of  rock  will  cost  from  50  cents 
to  $1.00,  according  to  its  hardness,  and  the  disposition  of 
its  seams. 

The  following  table  shows  the  number  of  cubic  yards 
which  can  be  loosened,  loaded,  &c.,  by  an  average  la- 
borer, in  a  day  of  10  hours.* 


NATURE    OF  THE 
WORK. 

CHARACTER    OF   THE    MATERIAL. 

Common 
Earth. 

Loose  and 
light  earth. 

Mud. 

Clay  and 
stony  earth. 

Compact 
Gravel. 

Rock, 
(blasted) 

Digging  up,  or 
Loosening. 

18 
to 
23 

16 

9 

7 
to 
11 

2.4 

Excavation  ;  in- 
cluding throw- 
ing 6  to  12  feet. 

8 
to 
12 

8 

7 
to 
16 

4 

2.2 

!  Loading  in  bar- 
rows. 

22 

8 

19 

Transport  by  bar- 
rows ;  per  hun- 
dred feet. 

20 
to 
33 

24 

to 
28 

Loading  in  carts. 

16 

to 
48 

17 

to 
27 

10 

Spreading      and 
Levelling. 

44 

to 

88 

25 

30 
to 
80 

*  Deduced  from  the  experiments  ol  M.  Ancelin. 


ESTIMATE    OF   COST.  127 

The  cost  per  cubic  yard  of  each  kind  of  labor  will  be 
readily  obtained  by  dividing  the  day's  wages  by  the  num- 
ber of  cubic  yards  in  the  table. 

The  cost  of  throwing  with  the  shovel  is  usually  one- 
third  of  that  of  digging  up. 

From  90  to  120  square  yards  of  surface  of  embank- 
ment can  be  "  trimmed  "  in  a  day. 

"When  the  net  cost  of  performing  any  work  has  been 
ascertained,  one-twentieth  of  it  should  be  added  for  the 
cost  of  tools,  superintendence,  <fcc.  ;  and  one-tenth  of  the 
whole  for  the  profits  of  the  contractor. 

Distance.  The  third  element  in  the  price  of  earthwork 
is  the  distance  to  which  the  excavations  must  be  removed. 
If  the  road  be  on  a  side-hill,  and  be  so  located  that  the 
excavation  from  its  upper  side  can  be  at  once  thrown  over 
to  make  the  embankment  on  its  lower  side,  the  cost  will 
be  little  more  than  that  of  the  simple  excavation.  But 
usually  large  amounts  of  earth  require  to  be  removed  con- 
siderable distances,  with  great  increase  of  expense.  The 
methods  to  be  employed  will  vary  with  the  circumstances 
of  the  case,  as  will  be  explained  under  the  head  of  "  Con- 
struction." 

The  comparative  cost,  per  cubic  yard,  (according  to 
experiments  made  at  Fort  Adams,  Newport,  R.  I.,)  of  ex- 
cavating earth,  and  removing  it  to  various  distances,  with 
wheelbarrows,  one-horse  carts,  and  ox-carts,  is  given  by 
the  following  table,  which  includes  the  cost  of  looseniHg, 
filling,  and  dropping ;  and  estimates  a  laborer's  wages  at 
$1.00  per  day  of  10  hours;  a  horse,  cart,  and  driver,  at 
$1.34  per  day  of  9  hours ;  and  an  ox-team  and  driver 
$1.60  per  day  of  9  hours.  The  earth  was  ploughed  up 
at  a  cost  of  f  cent  per  cubic  yard. 


128 


THE    LOCATION    OP    ROADS. 


COST    IN  CENTS  PER  CUBIC  YARD. 

DISTANCES  IN  FEET. 

Wheelbarrow. 

One-horse  cart. 

Ox-cart. 

30 

5.5 

8.2 

8.6 

60 

6.9 

8.4 

8.8 

90 

8.2 

8.6 

89 

120 

9.5 

8.8 

9.1 

150 

10.9 

9.0 

9.3 

180 

12.2 

9.2 

9.4 

210 

13.5 

9.4 

9.6 

240 

14.8 

9.6 

9.8 

300 

17.5 

10.0 

10.1 

450 

24.2 

11.0 

10.9 

600 

30.8 

12.0 

11.8 

900 

44.1 

14.0 

13.4 

1200 

57.4 

16.0 

15.1 

1500 

70.7 

18.0 

16.8 

From  the  preceding  table  it  appears,  that,  with  its  data, 
the  cost,  after  loading,  of  removing  the  earth  100  feet, 
was,  in  barrows,  4.43  cents  per  cubic  yard  ;  in  one-horse 
carts,  .66  cent ;  and  in  ox-carts,  .56  cent. 

Some  accurate  experiments  on  the  Birmingham  and 
Gloucester  Railway*  make  the  cost  in  barrows,  per  IOC 
feet,  at  $1.00  per  day,  W0  =  3.4  cents  ;  the  experiments 
of  M.  Ancelinf  give  yy  to  W0  —  3  to  5  cents  ;  the  Ameri- 
can translator  of  Sganziojl  'TV  —  5£  cents. 

It  is  usual  in  barrow-work,  to  consider  any  vertical 
transport  of  the  earth  as  costing  eighteen  times  as  much 
as  the  same  number  of  feet  of  horizontal  distance  ;  though 
from  accurate  experiments  it  seems  that  the  ratio  should 
be  as  24  to  1  for  barrows,  and  as  14  to  1  for  horse 
carts.fy 


»  Laws  of  Excavation  and  Embankment  on  Railways,  p.  136. 
t  See  page  126  t  Page  110.  §  Gayffier,  p.  146. 


ESTIMATE    OF    COST.  120 

The  cost  of  transport  by  any  method  will  be  expressed 
by  the  formula — 

P  (2D  +  d) 

L  x  C 
in  which  P  =  price  of  day's  work  of  the  vehicle  and  its 

driver. 

D  =  mean  distance  of  transport. 
d  =  distance  which  could  have  been  gone  over 
in  the  time  consumed  in  each  filling  and 
emptying. 

L  =  the  distance,  which  would  be  gone  over  in 
a  day  by  the  vehicle,  proceeding  without 
interruption  at  its  average  pace  ;  usually 
between  twenty  and  twenty-five  miles, 
or  between  100,000  and  130,000  feet. 
C  =  the  cubic  contents  of  the  load,  expressed 

in  fractional  parts  of  a  cubic  yard. 
If  P  =  134,  D  =  1500,  d  =  1000,  L  =  100,000,  and  C  =  i, 

134(3000  +  1000) 

the  formula  becomes  -p-          — '— — =  =  10.7  cents.* 

100,000  X  -g 

The  complete  cost,  with  one-horse  carts,  of  excavating 
earth,  transporting  it,  and  forming  an  embankment,  is  very 
completely  expressed  in  a.  formula  enunciated  in  the  Jour- 
nal of  the  Franklin  Institute  for  September,  1841,  by 
Ellwood  Morris,  C.  E. 

The  average  pace  of  a  horse  carting  embankment  is 
taken  at  100  feet  of  trip,  and  back,  per  minute ;  and  the 
time  lost  in  loading,  dumping,  &c.,  at  four  minutes  per  load. 

For  the  variable  quantities  the  following  symbols  are 
employed  : — 

a  =  number  of  feet  in  the  average  haul,  or  "  lead,"  of 
the  embankment. 


»  For  a  table  thus  calculated,  see  Marlette,  p.  91. 

9 


130  THE  LOCATION  OF  ROADS. 

b  =  number  of  hours  worked  per  day. 

c  =  daily  wages  of  laborer,  in  cents. 

d  =     "         "  cart,  including  driver  and  all   ex- 

penses of  carting. 
e  =  cost  of  loosening  materials,  in  cents,  per  cubic 

yard  ;  ranging  from  one  to  eight,  as  stated  on 

page  125. 
f  =  number  of  cart-loads   required   to   form  a  cubic 

yard  of  bank.     Usually  3  on  a  descending  road, 

3£  on  a  level,  and  4  on  an  ascending  road. 
g  =  number  of  cubic  yards  which  a  medium  laborer 

will  load  into  a  cart  per  day,  ranging  from  ten 

to  fourteen,  as  stated  on  page  125. 
Then  the  minutes  in  the  day's  work  =  60  b  ; 

The  minutes  consumed  in  each  trip  =  —  —  ; 

100 

The  number  of  trips,  or  loads  hauled  per  day,  is 
606 


The  number  of  cubic  yards  hauled  per  day,  is 
606 


The  cost  of  hauling,  per  cubic  yard,  is 

^        _^(l5o  +  4) 

~606~"  [AJ' 


Adding  to  this  the  cost  of  excavation  =  —  ,  that  of 

S 

loosening  =  e,  and  that  "of  trimming  =  1  cent,  we  obtain 
for  the  total  cost  of  a  cubic  yard  of  embankment, 


ESTIMATE    OF    COST.  131 


+ 1          [B]. 


Applying  it  to  an  actual  case,  in  which  a  =  1000, 
b  =  10,  c  =  125,  d  =  175,  e  =  2i,  /=  3i,  g=  12, 
the  formula  [A]  for  the  cost  of  hauling,  becomes  — 

"•><•  * 


and  the  formula  [B],  for  the  total  cost  of  a  cubic  yard  of 
embankment,  becomes  — 

125 
2.5  +  —  +  14.3  +  1  =  28.2  cents. 

The  actual  cost,  with  these  data,  on  an  amount  01 
22,000  yards,  was  27.9  cents,  differing  from  the  calcula- 
tion only  three-tenths  of  a  cent  ;  and  on  a  total  amount  of 
150,000  yards,  the  actual  and  calculated  costs  in  no  case 
differed  more  than  one  cent. 

An  easy  approximate  rule  for  the  average  cost  of  haul- 
ing one  cubic  yard  any  distance  on  a  level,  with  such 
carts  and  rates  of  travel  as  those  above  referred  to,  may 
be  deduced  from  formula  A  :  — 

For  300  feet  divide  the  wages  of  cart  and  driver  by  24 
500    "  "  «  19 

1000    "  "  "  12 

1500    "  "  "  9 

2000    "  "  "  7 

2500    "  "  "  6 

3000    "  "  "  5 

The  greater  the  distance  of  the  haul,  the  less  is  the 
proportional  cost,  in  consequence  of  less  time  being  lost 
m  filling  and  dropping. 


132  THE  LOCATION  OF  ROADS, 

In  excavation  and  embankment  with  the  scraper  01 
scoop,  (the  use  of  which  will  be  explained  under  the  head 
of  Construction)  the  number  of  cubic  yards  moved  per  day 
of  ten  hours,  a  distance  expressed  by  a  feet  (adding  vertical 

height  to  horizontal  distance)  =  —    -Ofrr-*  If  the  wages  of 
d  T  93]2 

scraper  and  driver  be  denoted  by  c  cents,  and  cost  of  loosen 
ing  by  d,  the  cost  per  cubic  yard  =^+C^a  .    When 

a  =  55,  c  =  275,  and  d  =  1,  the  cost  becomes  — 


When  an  embankment  is  made  of  earth  carried  beyond 
a  certain  distance,  (usually  100  feet  in  the  direction  of  the 
length  of  the  road)  it  is  paid  for  twice  ;  once  as  excava- 
tion and  once  as  embankment,  according  to  prices  previ 
ously  stipulated  ;  but  when  carried  less  than  this  distance, 
(as  when  thrown  from  the  upper  to  the  lower  side  of  a  road 
which  is  half  in  cutting  and  half  in  filling)  only  one  price, 
that  of  the  excavation,  is  estimated  for  ;  and  the  amount 
of  embankment  in  this  situation  must  be  subtracted  from 
the  total  amount,  before  multiplying  this  by  the  embank- 
ment price.  If  a  portion  of  an  embankment  is  required 
to  be  made  of  some  peculiar  material,  which  can  be  ob- 
tained only  from  a  greater  distance  than  the  other  materials 
of  the  bank,  a  separate  and  higher  price  should  be  estima 
ted  for  it. 

In  our  estimate,  thus  far,  we  have  determined  only  the 
cost  of  the  excavation  and  embankment. 

The  land  to  be  occupied  by  the  road  is  another  impor- 
tant item.     The  quantity  to  be  taken  having  been  calcu 


»  Journal  of  Franklin  Institute.  October,  1841. 


ESTIMATE    OF    COST.  133 

laietl,  with  due  allowance  for  the  extra  width  of  the 
cuttings  and  fillings,  is  to  be  reduced  to  acres  in  agricul 
tural  districts,  and  to  square  feet  in  towns  and  villages. 
Its'  value,  if  not  settled  by  agreement,  must  be  determined 
by  appraisers,  who  are,  however,  naturally  too  much  in- 
clined to  favor  the  interests  of  private  individuals  to  the 
prejudice  of  the  company,  or  public  body,  which  con- 
stitutes the  opposite  party,  subjecting  them  to  the  pay- 
ment of  extravagant  compensations. 

The  cost  of  fencing  will  vary  with  the  locality. 

The  mechanical  structures,  as  bridges,  culverts,  &c,  if 
numerous  and  large,  add  greatly  to  the  cost  of  the  road  ; 
but,  if  important,  must  be  confided  to  a  professional  engi- 
neer. 

The  stonework  is  usually  paid  for  by  the  cubic  yard, 
but  in  some  parts  of  the  country  by  the  "  perch,"  of  25 
cubic  feet.*  Wood  is  paid  for  by  the  cubic  foot,  or 
"  solid  measure,"  when  no  one  of  its  dimensions  is  as 
small  as  some  conventional  limit,  which  is  usually.  4 
inches  ;  but  "  board  measure"  (one-twelfth  of  the  former) 
is  employed  when  the  wood  is  4  inches,  or  less,  in  any  of 
its  dimensions.  "  Running  measure,"  referring  to  length 
only,  is  used  for  simple  constructions,  which  have  small 
and  regular  cross-sections,  a»  ditches,  piles,  &c. 

The  Engineering  expenses,  including  laying  out,  super- 
intendence, office-work,  &c.,  are  usually  estimated  at  10 
per  cent,  upon  the  amount  of  the  other  items. 

Every  possible  source  of  expense  should  be  taken  into 
the  account,  and  an  ample  price  for  each  allowed  ;  but, 
finally,  at  least  10  per  cent ,  upon  the  total  amount,  must 
be  added  for  Contingencies. 

*  More  precisely  24J  feet,  its  standard  being  a  rubble  wall,  1CJ  feet 
long,  and  18  inches  thick. 


134  THE  LOCATION  OF  ROADS. 

E  ren  then  the  actual  expense  will  generally  exceed  the 
estimate.*  For  this  opprobrium  of  the  engineering  pro- 
fession there  are  many  causes. 

The  price  of  labor,  as  the  work  proceeds,  particularly 
if  it  be  one  of  magnitude,  may  rise  far  above  what  it  was 
at  the  time  of  the  estimate. 

In  a  deep  cutting,  rock  may  be  found,  where  earth  was 
expected,  and  the  cost  of  that  part  of  the  excavation  will 
therefore  be  increased  tenfold. 

Many  improvements  in  the  plan  of  the  work  are  sug- 
gested and  adopted  as  it  proceeds  ;  almost  always  with  an 
increase  of  cost. 

Finally,  it  must  be  confessed  that  many  incidental  ex- 
penses, trifling  in  themselves,  but  considerable  in  their 
aggregate,  rarely  fail  to  be  overlooked  in  the  original  es- 
timate. 


8.  FINAL  LOCATION  OF  THE  LINE. 

When  the  preceding  operations  of  measuring,  mapping, 
and  calculating,  have  been  performed  upon  each  of  the 
various  lines  of  communication  between  the  two  extremi- 
ties of  the  route,  which  have  been  considered  worth  sur- 
veying, their  relative  merits  are  to  be  examined.  One 
may  be  shorter ;  another  more  level ;  a  third  may  require 
less  earthwork,  and  so  on.  The  good  and  bad  points  of 
each  route  are  to  be  compared  by  the  principles  laid  down 
on  pages  68  and  69,  and  that  one  adopted  which  will  en 
able  the  most  labor  to  be  performed  on  it  with  the  least 

*  On  the  twenty  principal  railroads  in  England,  the  average  proportioix 
ol  the  actual  cost  to  the  original  estimate  was  as  2|  to  1.  The  least  va- 
riation was  62  per  cent  excess ;  in  the  greatest,  the  cost  was  nearly  gix 
times  the  estimate. 


RECTIFICATION.  135 

number  of  horses,  provided  the  expense  of  its  construc- 
tion fall  within  the  limits  established  by  calculation,  or  by 
necessity.*  The  persons  who  are  to  make  the  selection 
and  decision  should  have  before  them, 

1.  A  general  map  of  the  localities. 

2.  A  profile  of  each  line. 

3.  Cross-sections  at  short  intervals. 

4.  The  calculations  of  excavation  and  embankment 

5.  Drawings  of  the  bridges,  culverts,  &c. 

6.  Specifications  of  all  the  works. 

7.  Amounts  of  stone-work,  timber,  &c 

8.  Analysis  of  the  prices  of  each. 
9    Estimate  of  cost. 

10.  Estimate  of  revenue. 

11.  Descriptive  memoir. 

The  final  location  of  the  line  adopted  is  then  to  be 
made.  It  consists  chiefly  in — 

1 .  Rectification  of  the  straight  portions  of  the  line 

2.  Laying  out  its  curves. 

3.  Staking  out  its  side-slopes. 

RECTIFICATION'. 

The  minor  irregularities,  bends,  and  zigzags  of  the  line 
(caused  in  part  by  the  transverse  balancing)  may  often  be 
removed  by  substituting  for  them  one  straight  line,  which 
will  be  the  average  of  their  deviations  on  either  side.  A 
ilagstaff  being  placed  at  one  end  of  the  line,  an  observer, 
at  the  other  end,  by  signals  directs  assistants  to  place  "  in 
line"  the  rods  which  they  bear  ;  and  the  points  thus  found 
are  marked  by  stakes,  which  are  usually  driven  at  every 
hundred  feet.  In  the  case  of  long  lines,  through  a  coun- 

»  Parnell,  pp.  322,  433- 


130  THE  LOCATION  OF  ROADS. 

try  of  forests,  the  use  of  the  compass,  or  some  other  angu- 
lar instrument,  is  almost  indispensable,  for  it  is  still  an  un- 
solved problem  in  engineering,  how,  without  the  aid  of 
these,  the  Romans  attained  the  wonderful  straightnesi? 
with  which  they  carried  their  roads  over  thickly-wooded 
hills  and  valleys,  with  such  lofty  disdain  of  the  effects  of 

gravity. 

Fig.  60. 


When  a  hill  rising  between  two  points,  as  A  and  B,  pre- 
vents one  being  seen  from  the  other,  two  observers  C  and 
D  may  place  themselves  on  the  ridge,  as  nearly  as  possible 
in  the  line  between  the  two  points,  and  so  that  each  can  at 
once  see  the  other  and  the  point  beyond.  C  looks  to  B,  and 
by  signals  puts  D  "  in  line."  D  then  looks  to  A,  and  puts 
C  in  line.  C  repeats  his  operation,  and  so  they  alter- 
nately "  line"  each  other,  continually  approximating  to  the 
straight  line  between  A  and  B,  till  they  at  last  find  them- 
selves both  exactly  in  it. 

When  a  wood,  or  some  such  obstacle,  intervenes  between 
the  two  points,  as  in  Fig.  61,  a  different  method  must  be 
adopted.  The  direction  from  A  to  B  not  being  exactly 
known,  leaving  a  rod  at  A,  set  up  another  at  C,  as  nearly  in 
the  desired  line  as  possible.  Go  on  as  far  as  the  two  rods 
at  A  and  C  can  be  seen,  and  set  up  another  at  D,  "  in  line" 
with  A  and  C  Go  on  beyond  D,  and  place  another  rod, 


CURVES. 

Fig.  61. 


E,  in  line  with  D  and  C  ;  and  so  proceed,  producing  the 
straight  line  till  it  arrives  at  Z,  opposite  B.  Measure  the 
distance  ZB,  and  move  the  stakes  C,  D,  E,  &c.,  towards 
the  true  line  by  a  quantity  proportional  to  their  distances 
from  A.  Thus  if  AZ  be  1000  feet,  and  ZB,  the  final 
divergence,  be  ten  feet,  a  stake  C,  200  feet  from  A, 
should  be  moved  two  feet  to  C',  in  order  to  bring  it  into 
the  true  line  AB ;  and  so,  proportionally,  with  the  rest. 


The  angles,  which  are  formed  by  the  meeting  of  the 
straight  lines  established  in  the  approximate  location  of 
the  road,  must  be  rounded  by  curves,  to  which  the  straight 
lines  must  be  tangents  at  their  points  of  junction. 

On  every  curve  there  is  an  unavoidable  loss  of  power 
in  the  deflection  of  vehicles  from  the  straight  line  which 
all  bodies  in  motion  tend  to  follow ;  and  there  is  danger 
from  the  effects  of  the  centrifugal  force.  The  resistance 
is  inversely  as  the  radius  of  the  curve,  i.  e.,  greater  as  the 
radius  of  the  curve  is  smaller ;  for  the  force  required  to 
draw  a  carriage  around  a  curve  may  be  considered  as 
composed  of  two  portions ;  one  equal  to  the  force  which 
would  l)e  required  to  draw  it  over  a  straight  line  of  the 
same  length  as  the  curve,  and  the  other  dependent  on  the 
additional  power  necessary,  at  each  instant,  to  draw  it 
into  the  curved  line  from  the  tangent  in  which  it  tends  to 


138 


THE    LOCATION    OF    ROADS. 


move.  A  certain  amount  of  force  being  required  to  pro- 
duce the  entire  change  in  direction,  the  smaller  the  radius 
of  a  curve,  the  less  space  and  time  is  given  for  the  exer- 
cise of  this  force,  and  a  larger  share  of  it  roust  therefore 
be  exerted  at  each  moment,  with  a  great  increase  of  labor 
and  danger. 

It  is  therefore  very  important  that  every  road-curve 
should  have  as  great  a  radius  as  possible.  It  should 
never  be  less  than  one  hundred  feet.  - 

When  a  curve  is  necessary  upon  a  steep  grade,  the  in 
clination  should  be  flattened  at  that  place  in  order  to  com- 
pensate for  the  additional  resistance  of  the  curve.  On 
this  account  a  zigzag  line  up  a  hill  is  more  objectionable 
than  an  oblique  ascent  by  a  straight  line. 

The  curves  which  are  employed  to  unite  straight  lines 
are  usually  either  circular  or  parabolic  arcs. 

CIRCULAR    ARCS. 

Having  given  two 
straight  lines  meeting 
at  C,  (or  which  would 
so  meet,  if  produced) 
it  is  required  to  mark 
out  on  the  ground  an 
arc  of  a  circle  to  which 
these  lines  shall  be 
tangents. 

The  simplest  mode 
for  an  arc  of  small  ra- 
dius would  be  to  find  the  centre,  by  erecting  perpendicu 
lars  to  the  tangent  lines  at  equal  distances,  A  and  B,  from 
their  point  of  meeting  C.  The  intersection,  O,  of  the 
perpendiculars  would  be  the  centre,  from  which  the  arc 


CURVES.  139 

might  be  swept  with  a  cord  of  proper  length.  But 
curves  are  often  employed  with  a  radius  of  one  or  more 
miles,  so  that  this  method  would  seldom  be  practicable 
The  curve  must  therefore  be  traced  independently  of  its 
centre. 

In  practice,  instead  of  a  circle,  a  polygon  is  marked 
out,  with  sides  or  chords  each  one  hundred  feet  long. 
Stakes  are  set  at  the  ends  of  each  of  these  chords,  and 
are  therefore  in  the  circumference  of  the  desired  circle. 
The  chords  themselves,  in  circles  of  large  radius,  will 
nearly  coincide  with  the  arcs. 

The  question  is  now,  in  what  manner  to  fix  the  position 
of  these  chords.  Two  methods  are  in  common  use  ;  one 
by  "  angles  of  deflection,"  and  the  other  by  "  versed 
sines."  The  former  is  generally  employed  upon  railroads, 
but  requires  the  use  of  an  angular  instrument.*  The 
latter  dispenses  with  this,  and  is  therefore  the  one  which 
will  be  here  explained. 

Fig.  63. 


•  For  its  details  and  other  methods  of  running  curves,  see  Appendix  C. 


HO  THE    LOCATION    OF    ROADS 

The  stations  are  supposed  to  be  at  equal  distances 
(each  of  which  is  usually  a  chain  of  100  feet)  and  the 
versed  sine  to  be  given,  or  to  have  been  found  by  trial. 
Assume  it  at  two  feet,  and  let  station  2  be  the  point  at 
which  the  c  irve  is  to  begin.  From  station  2  measure  in- 
ward, towards  the  centre,  half  the  versed  sine  (or  one 
foot)  to  2',  and  place  there  a  rod.  Stretch  out  the  chain 
from  2,  and  bring  its  farther  extremity  into  the  line  of  2 
and  the  back  station  1,  and  it  will  fix  station  3,  at  which  a 
stake  is  to  be  driven.  From  3  measure  inward  the  full 
versed  sine  to  3'  ;  draw  on  the  chain  till  its  extremity  is  in 
line  with  3'  and  2,  and  it  fixes  station  4.  So  proceed, 
measuring  inward  the  full  versed  sine,  at  each  station,  till 
you  arrive  at  the  station  (5,  in  the  figure)  where  it  is  de- 
sired to  end  the  curve,  and  to  pass  off  on  a  tangent. 
There  only  half  the  versed  sine  is  to  be  used.  Station  6 

is  thus  found,  and  the  line  5 6  gives  the  direction  of  the 

final  tangent,  as  2 1  gave  that  of  the  initial  one.  The 

stations  2,  3,  4,  5,  thus  found,  will  be  points  in  the  cir 

cumference  of  a  circle  to  which  the  lines  1 2  and  5 0 

are  tangents. 

To  find  approximately  intermediate  points,  measure 
outwards  from  the  middle  of  each  chord,  a  secondary 
versed  sine  =  one  fourth  of  the  original  versed  sine.  If 
more  points  are  required,  measure  from  the  middle  of  the 
new  chord,  a  tertiary  versed  sine  =  one  fourth  of  the 
secondary  one  ;  and  so  on. 

The  versed  sine  has  been  thus  far  supposed  to  be 
known.  To  calculate  it  from  the  angle  of  two  meeting 
lines,  the  following  problems  are  required. 

Problem  1.  To  find  the  radius  of  the  circular  arc  which 
unites  two  straight  lines  meeting  at  a  given  angle,  the  distance 


CIRCULAR    ARCS. 

from  their  intersection                          Fig. 
to  the  initial  and  final 
points    of   the    curve                               J 
being  also  given.                         ^>^f-~  —  i 

64 

% 
5  "i^^i*. 

is  the  given  angle,  and              \ 
A  and   B   the   initial                \ 
and    final    points,    at                  \ 
equal   distances   from                    \ 
the  point  of  intersec-                      \ 
tion.       The     triangle                        \ 
CBO,  right-angled  at                        \ 
B,  gives                                                \ 
tan.BCOxBC                              \ 

* 

/ 

rad.           '  '•  e'                         \ 

141 


The  required  radius  is  equal  to  the  natural  tangent  (to  radius 


unity)  of  half  the  given  angle, 
multiplied  by  the  distance  from 
the  intersection  to  the  beginning 
or  ending  of  the  curve.* 


Fig.  65. 


Problem  2.  To  find  the  versed 
sine,  having  given  the  radius. 

Given  the  radius  OA  or  OF, 
and  any  two  equal  chords,  AE, 
and  EF,  required  the  versed 
sine  ED. 

ED'  =  AE'  —  AD1 
AD'  =  AO'  —  DO'  =  AO'  —  (EO  —  ED)'  — 

=  AO'  —  (AO  —  ED)'  = 

=  AO1  —  AO'  +  2AO  .  ED  —  ED'  =  2AO  .  ED  —  ED'. 

.-.ED'  =  AE'  —  2AO  .  ED  +  ED* 

2AO  .  ED  =  AE' 


--- 
2AO  ' 

i.  e.,  the  versed  sine  is  equal  to  the  square  of  the  chord,  di- 
vided by  twice  the  radius.  When  AE  •.=  100  feet,  the  versed 
»ine  is  equal  to  5000  feet  divided  by  the  number  of  feet  in  the 

*  AC  and  AB  being  known,  Radius  OA  =  ^^ 


142  THE  LOCATION  OF  ROADS. 

radius.     When  ^.E  =  66  ieet,  the  versed  sine  equals  2178 
feet  divided  by  the  radius. 

When  the  lines,  which  are  to  be  united  by  a  curve,  do 
not  actually  meet,  the  angle  which  their  directions  form 
may  be  readily  calculated  ;  but  after  a  little  practice  it 
will  be  easier  to  assume  some  versed  sine ;  to  run  a  trial 
curve  with  it ;  and  after  ascertaining  whether  it  be  too 
large  or  too  small,  to  assume  another  nearer  the  proper 
)ne,  and  so  proceed. 

Compound  Curves.  The  above  method  supposes  that 
the  curve  has  the  same  radius,  or  degree  of  curvature, 
throughout,  and  that  it  unites  the  two  tangents  at  equal 
distances  from  their  intersection.  But  it  is  often  required 
to  increase  or  to  lessen  the  degree  of  curvature,  and  thus 
to  form  a  "  compound  curve,"  as  in  the  figure.  To  effect 
this,  at  the  station  where  the  change  Fig.  66. 

is  to  be  made,  use,  for  measuring 
inward,  half  the  sum  of  the  old  and 
new  versed  sine,  and  thence  pro- 
ceed with  the  new  one  only.  Thus, 
if  2  feet  has  been  the  original 
versed  sine,  and  the  features  of 
the  ground  which  is  next  to  be 
passed  over  require  a  curve  of  6 
feet  versed  sine  to  be  employed,  at  the  desired  point  use 
a  versed  sine  of  4  feet,  and  thenceforward  one  of  6  feet.  If 
the  curvature  is  to  be  lessened,  the  same  rule  applies. 

Reversed  Curves.  It  is  sometimes  necessary  to  reverse 
the  direction  of  a  curve,  and  to  commence  curving  in  a 
contrary  manner,  without  allowing  a  straight  line  lo  in- 

*  It  is  often  desirable  to  know  how  far  the  curve  will  depart  from  the 
intersection  of  the  taofjent  lio.es.  In  figure  64,  the  distance  required 
=  FC  =  OC  -OF  =  V  (OAS  -f  ACS)  —  OA 


PARABOLIC    ARCS. 
Fig.  67 


143 


tervene.  At  one  chain  beyond  the  point  at  which  it  is 
desired  to  make  the  change,  place  a  stake  in  the  line  of 
the  two  last,  and  at  it  begin  to  use  the  proper  versed  sine 
in  the  contrary  direction. 


PARABOLIC    ARCS. 


The  following  method  furnishes  an  easy  means  of  ob- 
taining a  Parabolic  curve. 

Fig.  68. 


Divide  the  two  tangent  lines  1....  13,  and  1 3.. ..1 2,  (whethei 
of  equal  or  different  lengths)  into  the  same  number  oi  equal 
parts,  as  many  as  may  be  thought  necessary.  Number 
the  points  of  division  on  one  tangent  with  the  odd  num- 
bers 1,  3,  5,  &c.,  up  to  the  vertex;  and  on  the  other  tan- 
gent number  them,  from  the  vertex,  with  the  even  numbers 
2,  4,  6,  &c.  Join  the  points  1  and  2,  3  and  4,  5  and  6 


144  THE  LOCATION  OF  ROADS, 

and  so  on ;  and  the  inner  intersections  A,  B,  C,  D,  E,  wiK 
be  points  in  the  curve  desired. 

To  fix  the  points  of  this  curve  upon  the  ground,  tall 
stakes  must  be  placed  at  each  of  the  points  of  division  of 
one  of  the  tangent  lines,  and  two  men  be  stationed  on  the 
other.  One  places  himself  at  station  1,  and  directs  his 
eyes  to  station  2.  The  other  places  himself  at  3,  and 
looks  to  4.  A  third  man,  holding  a  rod,  is  moved,  by  al- 
ternate signals  from  each  of  the  others,  till  he  comes  to  a 
point  which  is  in  both  their  lines  of  sight  at  once.  This 
will  be  the  point  A.  The  man  at  1  now  passes  to  5,  and 
looks  to  6,  the  other  remaining  at  3.  The  rodman,  being 
again  placed  in  both  their  lines  of  sight,  thus  fixes  the 
point  B.  The  remaining  points  are  similarly  determined. 

The  Parabolic  curve,  though  little  used  in  this  country, 
is  generally  preferred  in  France,  and  has  the  following 
advantages  over  a  circular  arc. 

It  approaches  nearer  to  the  intersection  of  the  tangent 
lines ;  and  as  they  are  supposed  to  have  been  originally 
placed  on  the  most  favorable  ground,  the  less  the  curve 
deviates  from  them,  the  less  increase  of  cutting  and  filling 
will  it  cause.  The  more  numerous  the  divisions,  the 
nearer  does  it  approach  the  tangents. 

Its  curvature  is  least  at  its  beginning  and  its  ending,  so 
that  its  deviation  from  the  straight  line  is  less  strongly 
marked. 

It  can  join  two  straight  lines  of  unequal  length,  as  in 
the  figure  ;  while  a  circular  arc,  of  constant  radius,  re- 
quires both  the  tangents  to  meet  it  at  equal  distances  from 
their  intersection. 


SETTING    GRADE    PEGS. 


145 


SETTING  GRADE  PEGS. 


The  line  of  the  road  having  been  marked  out  by  the 
methods  which  have  now  been  given,  and  stakes  set  at 
the  end  of  every  chain,  small  "  level  pegs"  are  then  to  be 
driven  beside  them,  with  their  tops  at  the  surface  of  the 
ground,  and  their  heights  above  or  below  the  intended 
height  of  the  road  (i.  e.  its  "  grade  line")  are  to  be  ascer- 
tained by  a  levelling  instrument,  and  the  corresponding 
"  Cut"  or  "  Fill"  marked  upon  the  large  stakes. 

Another  form  of  the  levelling  field-book,  better  Adapted 
for  this  work  than  that  given  on  page  98,  though  less  safe 
for  beginners,  is  presented  below.  It  refers  to  the  same 
stations  and  levels,  noted  in  the  previous  form  of  page  98, 
and  shown  in  fig.  43. 


Sta. 

Dist. 

B.  S. 

Ht.  Inst. 
above 
Datum. 

F.  S. 

Total 
Heights. 

A 

0.00 

B 

100 

2.00 

+2.00 

6.00 

—4.00 

C 

60 

3.00 

—1.00 

4.00 

—5.00 

D 

40 

2.00 

—3.00 

1.00 

—4.00 

E 

F 

70 

50 

6.00 
2.00 

+2.00 
+3.00 

1.00 
6.00 

+1.00 
-3.00 

15.00 

18.00   j     -3.00 

in  the  above  form  it  will  be  seen  that  a  new  column  is 
introduced,  containing  the  Height  of  the  Instrument,  (i.  e. 
of  its  line  of  sight,)  not  above  the  ground  where  it  stands, 
but  above  the  Datum,  or  starting-point,  of  the  levels. 
The  former  columns  of  "  Ascent"  and  "  Descent"  are 
omitted.  The  above  notes  are  taken  thus.  The  height 
of  the  starting-point  or  "  Datum,"  at  A,  is  0.00.  The 
Instrument  being  set  up  and  levelled,  the  rod  is  held  at  A. 
The  Backsight  upon  it  is  2.00  ;  therefore  the  height  of 
the  Instrument  is  also  2.00.  The  rod  is  next  held  at  B. 
10 


146 


LOCATION    OF    ROADS. 


The  Foresight  to  it  is  6.00.  That  point  is  therefore  6.00 
below  the  instrument,  or  2.00— 6.00=  — 4.00  below  the 
datum.  The  instrument  is  now  moved,  and  again  set 
up,  and  the  backsight  to  B,  being  3.00,  the  Ht.  Inst.  is 
—  4.00+3.00=  — 1.00,  and  so  on  :  the  Ht.  Inst.  being  al- 
ways obtained  by  adding  the  backsight  to  the  height  of 
the  peg  on  which  the  rod  is  held,  and  the  height  of  the 
next  peg  being  obtained  by  subtracting  the  foresight  to 
the  rod  held  on  that  peg,  from  the  Ht.  Inst. 

When  the  road  is  level,  the  "  Cutting"  or  "  Filling"  at 
any  point  is  the  height  of  that  point  above  or  below  the 
level  line.  But  when,  as  is  generally  the  case,  the  road 
ascends  or  descends,  farther  calculation  becomes  neces- 
sary. The  following  is  a  form  of  Grade  book,  convenient 
for  beginners 


1 

^ 

Uist 

100 
100 
100 
100 

3 

4 

Ht.  Inst. 
above 
datum. 

+9.700 
+7.900 
+8.280 
+6.908 

5 

6 

7 

8 

^_ 

Ht.Inst. 
above 
Grade. 

5.400 
3.300 
3.680 
2.50S 

10 

11 

SUi. 

B.  S. 

9.700 
1.800 
3.480 
1.798 

F.  S. 

Ht.Peg 
above 
Datum. 

0.000 
+6.  '00 
+4.800 
+5.110 
-2.965 

Rise  or 
Fall  of 
Grade. 

+0.300 
+0.300 
Level. 
—  0.200 

Ht.grade 
above 
Datum. 

Cot 

1.800 
0.200 
0.510 

Fill. 
4.000 

7.365 

0 

1 
1 

3 
4 

3.600 
3.100 
3.170 
9.873 

+4.000 
+4.300 
+4.600 
+4.600 
+4.400 

16.778 

19.743 
16.778 

—2.985 

The  first  six  columns  are  similar  to  those  of  the  form 
just  given.  The  7th  column  g->es  the  rise  or  fall  of  the 
grade  for  each  distance.  The  8th  is  obtained  by  a  con- 
tinual addition  of  the  preceding.  The  9th  is  the  differ- 
ence of  the  8th  and  the  4th,  and  is  convenient  for  the 
subsequent  "  Staking  out  the  side  slopes."  The  10th 
and  11  th  are  the  difference  of  the  Gth  and  the  8th,  as  on 
page  11G.  On  staking  out  side^slopee,  see  p.  457. 


THE    CONSTRUCTION    0*    ROADS.  147 


CHAPTER  III. 

THE    CONSTRUCTION    OF  ROADS. 

1  The  torrent  stops  it  not ;  the  ragged  rock 
Opens,  and  lets  it  in  ;  and  on  it  runs, 
Winning  its  easy  way  from  clime  to  clime, 
Through  glens  lock'd  up  before." 


CONTRACTS. 

THE  actual  "  Construction"  of  a  road,  after  its  "  Lo- 
cation" has  been  completed,  may  be  carried  on  by  days' 
work,  under  the  superintendence  of  the  agents  of  the  com- 
pany, or  town,  by  which  it  has  been  undertaken  ;  but  it 
will  be  more  economically  executed  by  CONTRACT.  A 
"  Specification"  is  first  to  be  prepared,  containing  an  ex- 
act and  minute  description  of  the  manner  of  executing 
the  work  in  all  its  details.  Copies  of  it,  with  maps,  pro- 
files, and  drawings  of  the  proposed  road,  &c.,  are  to  be 
submitted  to  the  inspection  of  the  persons  desiring  to  un- 
dertake it,  who  are  to  be  invited  by  advertisement  to  hand 
in  sealed  tenders  of  the  prices  per  cubic  yard  (or  other 
unit  of  measurement)  at  which  they  will  agree  to  perform 
the  work.  The  proposals  are  opened  on  the  appointed 
day,  and  the  lowest  are  accepted,  other  things  being  equal. 
The  "  Contract,"  which  is  to  be  then  .signed  by  the  par- 
ties, should  :ontain  copious  and  stringent  conditions  as  to 
the  time  and  manner  of  performing  the  work  ;  stipulating 
when  it  is  to  be  commenced,  how  rapidly  to  progress,  in 
what  order  of  parts,  and  when  to  be  corrpleted  ,  which 


148 


THE    CONSTRUCTION    OF  ROADS. 


of  the  incidental  expenses  are  to  be  borne  by  the  con- 
tractor, and  for  which  he  is  to  be  remunerated  ;  in 
what  cases  material  carried  from  excavation  into  em- 
bankment is  to  be  paid  for  at  the  united  prices  of  both ; 
what  penalties  for  neglect  are  to  be  imposed ;  when  pay- 
ments for  work  done  are  to  be  made  ;  and  so  on  •  always 
remembering  that  every  thing  must  be  expressed,  and 
nothing  left  to  be  inferred.* 

The  specification  is  considered  to  form  part  of  the  con- 
tract, and  a  "  Bond"  is  appended,  by  which  the  contractor 
and  his  sureties  are  "  holden  and  firmly  bound"  in  a 
penal  sum,  "  this  bond  to  be  null  and  void,  if  the  said 
parties  shall  faithfully  execute  and  fulfil  the  accompany 
ing  Contract." 

Each  contract  should  include  such  a  length  of  road, 
called  "  a  section,"  (usually  half  a  mile  or  a  mile  long) 
that  materials  for  the  embankments  may  be  obtained  from 
cuttings  within  its  limits.  There  should  be  separate  con- 
tracts for  the  mechanical  structures  required.  The  works 
which  will  need  most  time  for  their  execution  should  be 
commenced  first ;  but  no  contract  should  be  let,  till  the 
land  which  it  includes  is  secured,  or  exorbitant  demands 
will  be  made. 

It  has  been  said  that  the  lowest  bid  is  usually  accepted, 
but  this  is  to  be  taken  with  great  qualifications.  The 

»  In  the  contracts  for  the  public  works  of  the  state  of  New  York,  one 
valuable  paragraph  comprehends  every  thing,  saying,  "  To  prevent  all 
disputes,  it  is  hereby  agreed,  that  the  engineer  shall  in  all  cases  determine 
the  amount  or  quantity  of  the  several  kinds  of  work  which  are  to  be  paid 
for  under  this  contract,  and  the  amount  of  compensation  at  contract  prices 
to  be  paid  therefor  ;  and  also  that  said  engineer  shall  iu  all  cases  decide 
every  question,  which  can  or  may  arise,  relating  to  the  execution  of  this 
contract  on  the  part  of  the  said  contractor,  and  his  estimate  and  decision 
shall  be  final  and  conclusive." 


EARTHWORK.  149 

skill,  competency,  character,  and  responsibility  of  the 
contractor  are  as  important  as  the  lowness  of  his  prices. 
A  skilful  and  experienced  contractor  will  often  make  a 
profit  on  a  work,  which  another  has  abandoned  after  con- 
siderable loss.  Bids,  less  than  the  actual  cost  of  the 
work,  are  often  made,  both  from  ignorance  and  from  kna- 
very. In  the  former  case,  if  the  proposals  were  accepted, 
the  contractor  would  be  ruined,  and  obliged  to  leave  the 
work  unfinished ;  in  the  latter,  he  would  hope  to  gain 
something  by  doing  first  the  easy  and  profitable  parts  of 
the  work,  and  then  abandoning  it.  Jn  both  cases  the 
remaining  portions  would  be  executed  at  greatly  in- 
creased expense.  Six  contracts  in  England  amounting  to 
$3,000,000  being  abandoned,  were  finished  by  the  com- 
pany, and  cost  them  $6,000,000.  The  engineer  should 
therefore  ascertain  the  lowest  amount  for  which  the  work 
can  be  done,  and  not  let  it  for  less. 

The  work  done  is  usually  paid  for  monthly,  according 
to  a  measurement  made  by  the  inspecting  engineer.  Five 
or  ten  per  cent  is  generally  retained  till  the  completion  of 
the  contract. 

The  two  main  divisions  of  the  operations  necessary  in 
the  construction  of  a  road,  are  its  earthwork  and  its 
mechanical  structures. 


1.  EARTHWORK. 

The  term  earthwork  is  applied  to  all  the  operations  in 
excavation  and  embankment,  whatever  the  material. 

REMOVAL    OF    THE    EARTH.     ' 

The  problem  which  is  to  be  solved,  both  in  theory  and 
practice,  is,  "  To  remove  every  portion  of  earth  from  the 


150  THE    CONSTRtfCTIOIn    OF    ROADS. 

excavation  to  the  embankment  by  the  shortest  distance,  in 
the  shortest  time,  and  at  the  least  expense." 

It  must  also  be  deposited  so  as  to  form  a  consolidated 
mass,  and  so  that  not  •  particle  of  it  will  need  to  be  again 
moved. 

The  problem  is  very  important  in  practice,  for  upon  its 
mode  of  solution  depends  a  large  portion  of  the  cost  of 
the  work ;  and  in  theory,  it  requires  the  aid  of  the  higher 
Calculus,  since,  to  satisfy  its  conditions,  the  sum  of  the 
products,  arising  from  multiplying  all  the  elementary  vol- 
umes of  earth  into  the  distances  which  they  are  carried, 
must  be  a  minimum. 

We  have  seen,  on  page  123,  that  in  the  simplest  case, 
that  in  which  the  whole  of  one  excavation  is  to  be  carried 
into  one  embankment,  we  may  use  the  product  of  the 
entire  mass  multiplied  by  the  distance  of  the  centres  of 
gravity  of  its  two  positions.  But  when  certain  portions 
of  a  cutting  are  to  be  deposited  in  spoil-banks  ;  others  to 
form  part  of  an  embankment,  of  which  the  remainder  is 
to  be  obtained  from  side-cuttings  ;  &c.,  it  does  not  appear 
a  priori  what  arrangement  would  give  a  minimum  ex- 
pense. In  a  few  cases  the  proper  course  is  evident ;  as, 
if  a  hill  is  to  be  cut  down,  and  its  materials  serve  only  to 
fill  up  a  valley,  and  are  in  excess,  the  excavation  from  its 
summit  is  clearly  the  portion  to  be  deposited  in  spoil- 
bank  ;  if  the  materials  are  insufficient  to  form  the  em- 
bankment, it  is  the  part  most  distant  from  the  hill  which 
should  be  formed  from  a  side-cutting  ;  if  the  excavation  is 
to  be  carried  in  two  different  directions  and  is  in  excess, 
it  is  the  part  of  the  middle  which  should  be  rejected  and 
deposited  in  spoil-bank. 

One  general  principle  of  transport  may  be  readily  de  • 
duced.  Let  ABCD  represent  the  plan  of  an  excavation 


REMOVAL    OF    THE    EARTH. 
Fig.  70. 


161 


--''  ,v*r 

-r^'*.*** 



from  which  the  embankment  EFGH  is  to  be  formed.  If 
the  volume  CDik,  instead  of  being  taken  to  GH/m,  should 
be  transported  to  EFon,  it  follows  that  the  embankment 
GHZm  must  be  obtained  from  a  portion  of  the  excavation 
beyond  the  line  ik,  and  that  the  paths  of  the  two  volumes 
will  cross  each  other,  which  is  therefore  a  disadvantageous 
disposition,  since  it  increases  the  distances  passed  over. 
Any  such  crossing  of  the  paths  of  the  volumes  trans- 
ferred, either  horizontally  or  vertically,  may  be  generally 
avoided  by  conceiving  the  solids  of  excavation  and  em- 
bankment to  be  intersected  by  parallel  planes,  such  as 
DCHG,  ik,  Im,  &c.,  and  by  transferring  the  partial  solids 
in  the  manner  indicated  by  the  boundaries  marked  out  by 
these  planes. 

In  many  cases  the  most  economical  distribution  of  the  earth, 

can  be  determined  only  by  p-     ^ 

a     special      construction. 

Thus    in  the  figure,  sup- 

pose   that  ear:h  is  to  be 

taken   fioir,   A   and  B  to 

form  embankments   at    C 

and   D;   it  is  required  to 

know  which  should  form 

the  embankment  at  C,and 

which  that  at  D.    To  bring 

the   case   within- the    ap- 
plication of  the  principle 


152          THE  CONSTRUCTION  OF  ROADS, 

Just  enunciated,  conceive  the  triangle  ABD  to  turn  around  the 
line  AB  as  on  a  hinge,  so  that  the  point  D  comes  to  occupy  a 
point  D',  symmetrical  with  its  former  position. 

It  is  now  evident  that  to  avoid  the  crossing  of  the  paths,  tho 
earth  from  A  must  be  taken  to  D',  (i.  e.  D)  and  the  earth  from 
B  to  C  ;  AD'  +  BC  being  less  than  AC  +  BD'.  If  the  point 
D'  had  fallen  beyond  C  the  reverse  would  have  been  proper. 
If  the  point  D'  had  fallen  within  the  triangle  ABC,  there  would 
be  no  crossing  in  either  mode  of  transport,  but  the  proper  one 
would  be  determined  by  a  similar  algebraic  condition.* 

The  choice  would  be  indifferent,  if 

BC  — AC  =  BD  — AD, 
or  if  AD  — AC  =  BD  — BC; 

for  then,  AD  +  BC  =  AC  -f  BD. 

Two  points,  A  and  B,  Fig.  72,  being  found  which  fulfil  this 
condition,  other  points  will  be  found  at  the  intersection  of  arcs 

Fig.  72. 


described  from  C  and  D  as  centres,  with  radii  of  which  the  dif- 
ferences are  respectively  equal  to  the  given  difference  AD— AC, 
or  BD  —  BC.  If  a  great  number  of  these  points  were  found, 
the  polygonal  line  ABEFG  would  become  an  hyperbola,  pos- 
sessing the  remarkable  property  of  so  dividing  the  transporta- 
tion, that  C  should  receive  all  the  excavation  from  one  side  of 
il,  and  D  all  from  the  other. 

Suppose  that  embankments  at  C  and  D,  Fig.  73,  are  to  be 
made  from  a  mass  of  earth  mnop,  just  equal  to  them  in  volume. 
The  minimum  of  expense  will  be  obtained  by  finding  the  curve 
AG,  which  shall  divide  the  area  rnnop  into  two  parts  equal  to 


*G'yffier,  p.  134. 


REMOVAL    OF    THE    EARTH. 


1*3 


C  E  D 

those  required  at  C  and  D,  and  which  shall  also  possess  the 
properties  enunciated  in  the  preceding  paragraph.  If  the  line  EF 
drawn  perpendicular  to  CD,  from  its  middle  E,  does  not  cut  off 
a  sufficient  portion  of  the  area  to  supply  D,  this  shows  that  the 
curve  will  be  concave  towards  C.  Then  divide  geometrically 
the  area  mnop  in  the  required  proportion,  by  a  straight  line  rs, 
inclined  approximately  as  the  curve  would  be,  and  adopt  its 
middle  point  as  a  point  of  the  curve.  Then  will  BD  —  BC  be 
the  constant  difference  of  radii  required  to  find  the  other  points 
of  the  dividing  curve. 

If  the  amount  of  embankment,  which  might  be  deposited  at 
C  and  at  D,  was  indefinite,  and  the  only  requirement  was  its 
most  economical  removal  from  mnop,  then  the  perpendicular  EF 
drawn  from  the  middle  of  CD,  would  divide  the  area  into  two 
portions,  which  should  be  removed  to  the  points  C  and  D  re- 
spectively nearest  to  each  of  them. 

On  similar  principles  may  all  such  problems  be  resolved. 
Modifications  of  them  are  required,  when  the  paths  cannot  be 
taken  at  will,  as  when  a  bridge,  or  an  opening  in  a  wall,  is  a 
point  through  which  all  th(!  paths  must  pass.  The  number 
of  bridges,  of  openings,  of  rc-aits,  &c.,  which  will  be  most  ad- 
vantageous, require  separate  investigations.* 


*  See  Gayffier,  pp.  137  to  142. 


154  THE    CONSTRUCTION    OF   ROADS. 

EXCAVATION. 

The  excavation  and  removal  of  earth  is  performed,  ac- 
cording to  circumstances,  by  ploughs,  scrapers,  barrows, 
carts,  wagons,  &c.,  each  of  which  will  be  successively 
considered. 

LOOSENIXO. 

Most  earth  will  require  to  be  loosened  with  ploughs, 
spades,  or  picks,  before  being  shovelled  into  the  barrow, 
or  cart,  in  which  it  is  to  be  removed.  The  side-hill 
plough  possesses  some  advantages.  The  picks  should 
be  two  feet  from  point  to  point,  not  more  than  ten  or 
twelve  pounds  in  weight,  and  very  deep  and  strong  in  the 
eye,  or  socket  of  the  handle.  Light  and  loose  soil  may 
however,  be  at  once  taken  up  with  the  shovel. 

When  the  excavation  is  deep,  the  loosening  may  be  fa- 
cilitated, with  a  great  saving  of  time  and  labor,  by  digging 
a  narrow  channel  to  a  depth  of  five  or  six  feet,  and  under 
mining  the  face  of  the  bank  thus  formed,  letting  it  fall  at 
once  into  the  barrows,  or  carts,  beneath  it.  Its  disruption 
is  hastened  by  wedges  driven  into  its  upper  surface.  The 
concussion  of  the  fall  breaks  up  the  mass  into  small  pieces, 
with  great  economy,  but  not  without  danger  to  the  work- 
men. 

In  the  ordinary  excavation,  in  which  the  earth  is  dug 
up,  the  united  cohesion  and  weight  must  both  be  ovei- 
come  ;  in  the  method  just  described,  the  weight  assists  in 
overcoming  the  cohesion.  Representing  the  force  of  co- 
hesion by  3,  and  that  of  the  weight  by  2  ;  if  both  are  to 
be  overcome,  as  in  the  usual  method,  their  resistance  will 
DC  3  +  2  =  5  ;  while  if  the  weight  be  made  to  assist  the 
workman,  the  resistance  will  be  only  3  —  2  =  1. 


EXCAVATION.  155 

Steam  has  been  applied  to  excavation,  and  a  machine 
co  structed,  which  can  dig  and  load  1000  cubic  yards  per 
day,  in  favorable  soil  at  an  annual  cost,  including  inter- 
est, wear  and  tear,  labor,  &c.,  of  $7,500,  making  the 

$7,500 
cost  per  cubic  yard,  =  *i  cents.* 


SCRAPER  OR  SCOOP. 

This  implement  may  be  used  with  much  advantage, 
when  the  earth  yields  readily  to  the  plough,  and  is  not  to 
be  moved  more  than  100  feet  horizontally,  'nor  to  be 
raised  to  vertical  heights  of  more  than  15  feet;  though 
these  limits  may  sometimes  be  exceeded.  The  slopes  ot 
the  banks  which  it  forms,  should  not  be  steeper  than  1| 
to  1.  It  usually  contains  TV  of  a  cubic  yard.f  The 
Fig.  74. 


ground,  except  when  soft  or  sandy,  requires  to  be  previ 
ously  ploughed.  The  scraper  is  drawn  by  two  horses, 
managed  by  a  boy.  The  driver  elevates  the  handles,  and 
the  iron-shod  edge  runs  under  the  loose  earth,  rising  up 

*  Journal  of  the  Franklin  Institute,  September,  1843. 
1  Ibid.  October,  1841. 


156          THE  CONSTRUCTION  OF  ROADS. 

again  as  soon  as  the  handles  are  released  upon  its  being 
filled.  It  then  runs  with  slight  resistance  upon  two  con- 
vex iron-shod  runners,  which  project  slightly  beyond  its 
bottom,  and  is  thus  drawn  to  the  place  of  deposite.  At 
that  point  the  driver  raises  the  handles  ;  its  front  edge 
catches  in  the  earth,  and  its  forward  motion  overturns  it, 
and* discharges  its  load.  The  horses  keep  moving;  and 
the  scoop  is  dragged  back  to  the  place  of  excavation,  in 
its  inverted  position,  the  handles  resting  on  the  tree.  It 
is  there  loaded,  &c.,  as  before. 

BARROW-WHEELING. 

For  excavations  of  moderate  depths,  and  for  distances 
within  certain  limits,  barrows  are  most  conveniently  em- 
ployed. To  facilitate  emptying  their  contents,  the  bar- 
rows are  made  very  shallow,  with  splaying  sides,  and  with 
a  very  short  axis  to  the  wheel.  They  contain  from  ^5-  to 
TV  of  a  cubic  yard.  They  are  wheeled  on  "  runs"  of 
plank,  (as  long  and  thick  as  possible)  laid  on  the  ground, 
or  supported  on  trestles,  or  horses,  numerous  enough  to 
prevent  vibration.  When  the  tracks  are  inclined,  as  in 
ascending  from  a  deep  excavation,  they  should  be  laid 
with  a  slope  of  one  in  twelve.*  A  steeper  slope  fatigues 
the  workman  excessively;  a  flatter  one  increases  too 
much  the  length  of  his  route.  The  same  man  does  not 
usually  dig,  shovel,  and  wheel,  but  great  advantages  are 
obtained  by  a  division  of  labor.  One  man  picks,  (if  that 
be  required)  a  second  shovels  into  the  barrow  which  stands 
on  the  edge  of  the  excavation,  and  a  third  wheels  the  bar- 
row to  the  place  of  deposite,  or  to  the  next  "  stage,"  ac- 
cording to  the  distance.  In  the  latter  case,  at  the  end  of 

*  DUPIN.     Applications  de  la  Geometric. 


BARROW-WHEELING  157 

the  "  stage,"  he  meets  another  wheeler,  returning  jvith  an 
empty  barrow.  The  two  there  exchange  their  barrows  ; 
the  second  man  wheels  on  the  loaded  one  over  another 
stage,  while  the  first  man  returns  with  the  empty  barrow 
to  the  excavation,  where  he  finds  a  loaded  one,  which  has 
been  filled  during  his  absence  ;  and  so  the  circulation 
continues. 

The  length  of  the  "  stage"  should  be  such,  that  the 
time,  taken  by  the  wheeler  to  travel  over  it  with  a  loaded 
barrow,  and  lo  return  with  an  empty  one,  should  be  just 
sufficient  to  enable  the  shoveller  to  fill  the  barrow  left  at 
the  excavation.  It  should  vary  therefore  with  the  nature 
of  the  soil ;  lessening,  if  this  be  easily  worked,  and  in- 
creasing, if  it  offer  greater  resistance.  On  a  level  the 
length  of  a  stage  is  usually  from  60  to  100  feet.  On  an 
ascent  of  1  in  12,  it  should  be  diminished  by  one-third  ; 
on  a  similar  descent  it  should  be  increased  by  the  same  ; 
foj:  with  this  slope  the  labor  on  an  ascent  of  60  feet  ex- 
actly equals  a  level  stage  of  90  feet.* 

If  the  distance  were  not  divided  into  stages,  and  one 
man  wheeled  his  barrow  the  entire  length,  a  number  of 
runs  would  require  to  be  laid  from  the  excavation.  Such 
an  arrangement  would  be  inconvenient,  from  its  blocking 
up  the  work,  and  expensive,  from  the  cost  of  the  plank. 
At  the  point  where  the  run  terminates  in  the  excavation, 
two  planks  are  placed,  diverging  like  the  letter  Y»  the 
full  and  the  empty  barrow  being  wheeled  on  each  alter- 
nately. At  the  meeting  of  two  stages,  a  double  track  is 
laid,  to  form  a  turning-out  place  for  the  exchange  of  the 
barrows.  At  the  place  of  deposite,  several  planks  should 
radiate  from  the  main  track,  so  that  the  earth  may  be  at 

*  Dupin.     Applications  dc  la  Geometric. 


158          THE  CONSTRUCTION  OF  ROADS. 

once  evenly  distributed,  by  being  emptied  from  each  in 
turn,  thus  saving  much  subsequent  levelling. 

Barrow-wheeling  becomes  too  expensive  after  reaching 
a  certain  limiting  distance  of  transportation.  The  frequent 
neglect  of  this  consideration  leads  to  much  waste  of  labor. 
When  earth  is  to  be  conveyed  great  distances,  carts  or 
wagons  should  be  employed.  The  limit  is  determined 
by  a  combination  of  the  cost  of  filling  and  of  transporting. 
The  table  on  page  128,  makes  it  100  feet;  the  limit  in 
France,  with  barrows  containing  ^V  of  a  cubic  yard,  should 
be  200  feet ;  on  English  works,  with  barrows  holding  TV 
of  a  cubic  yard,  the  limit  is  300  feet.  The  limiting  dis- 
tance becomes  smaller  as  the  height  to  which  the  earth 
is  moved  becomes  greater.* 

CARTS,  ETC. 

One-horse  carts  may  be  advantageously  employed  for 
distances  exceeding  the  sphere  of  barrows.  For  short 
distances,  the  greater  proportional  loss  of  time  in  filling 
them  more  than  balances  their  economy  while  moving. 
They  should  be  made  very  light,  and  their  box  be  bal- 
anced on  a  pivot,  so  that  when  loaded  they  will  tend  to 
discharge  themselves.!  As  the  distance  increases,  wag- 
ons, drawn  by  two  horses,  become  cheaper,  and  a  tempo- 
rary railway  may  often  be  constructed  with  profit. 

When  the  length  of  the  lead,  (i.  e.  the  distance  from 
the  face  of  an  excavation  to  the  head  of  an  embankment) 
exceeds  1£  miles,  and  the  amount  of  earthwork  is  con- 
siderable, a  locomotive  engine  may  be  advantageously 
employed  to  draw  trains  of  wagons  upon  the  rails. 

*  Gayffier,  p.  159. 

t  When  horses  draw  loads  out  of  an  excavation,  the  inclination  of  theil 
track  should  not  exceed  1  in  20.  DUPIN.  Applications  de  la  Qeometrie 


CARTS,    ETC.  159 

"  Casting  up  by  stages"  is  a  method  sometimes  em- 
ployed for  removing  the  earth  from  deep  excavations.  A 
scaffold  is  prepared  with  a  number  of  platforms,  each  five 
feet  above  the  other,  and  each  successive  one  receding, 
like  the  steps  of  a  staircase.  On  each  platform  stands  a 
man  with  a  shovel.  The  laborer  in  the  excavation  throws 
the  earth  upon  the  first  platform  ;  the  man  there  stationed 
throws  it  up  to  the  second  ;  and  so  on  in  succession  till  it 
reaches  the  surface. 

Horse-runs  are  also  resorted  to  in  very  deep  excava- 
tions, where  the  banks  are  necessarily  very  high  and  steep. 
Upon  the  slope  of  the  bank  are  placed  two  plank  "  runs," 
or  tracks,  reaching  from  the  top  to  the  bottom  of  the  ex 
cavation.  The  distance  between  them  must  be  a  little 
greater  than  the  depth  of  the  excavation.  At  the  top  of 
each  is  a  pulley,  over  which  plays  a  rope,  the  ends  of 
which  pass  down  the  runs.  Each  end  of  the  rope  is 
fastened  to  the  front  of  a  barrow,  and  its  length  is  so  ad- 
iusted  that  one  barrow  will  be  at  the  top  of  one  run,  while 
the  other  barrow  is  at  the  bottom  of  the  other  run.  At 
the  top  of  the  excavation,  a  horse,  attached  to  the  rope, 
travels  horizontally,  alternately  raising  one  barrow,  which 
has  been  filled  below,  and  lowering  the  other,  which  has 
been  emptied  at  the  top.  A  man  has  hold  of  each  bar- 
row to  guide  it  in  its  ascent  and  descent,  the  weights  of 
the  men  balancing  each  other.  This  method  is  advan- 
tageous for  depths  exceeding  20  feet.*  The  use  of  bar- 
rows in  such  cases,  with  the  proper  inclinations  for  the 
runs  would  require  loo  great  a  distance  to  be  travelled 
over. 

•  Gauthey,  ii.  197. 
11 


160  THE    CONSTRUCTION    OF    ROADS. 

SPOIL-BANKS. 

The  spoil-banks,  formed  by  the  deposites  of  the  sur- 
plus earth  of  an  excavation,  are  usually  shaped,  as  in  the 

Fig.  75. 


figure,  with  side-slopes  of  H  to  1.  If  the  land  which 
they  occupy  be  of  little  value,  it  will  be  economical  to  ex- 
tend them  along  the  line  AB,  making  them  wider  and 
lower  within  certain  limits  ;  since  vertical  transport  costs 
so  much  more  than  horizontal.*  The  solution  of  the 
problem  of  minimum  expense  shows  that  for  spoil-banks 
made  with  barrows,  (slopes  \\  to  1,  and  employing  the 
customary  ratio  of  18  to  1,  for  the  comparative  expense 
of  horizontal  and  vertical  transport)  the  base  AB  should 
be  fifteen  times  the  height.t 

SIDE-SLOPES. 

To  preserve  the  slopes  of  deep  excavations  from  being 
gullied  and  washed  down  into  the  road,  a  ditch  should  be 
made  along  the  upper  edges  of  llie  cutting,  in  order  to 
prevent  the  surface  water  of  the  "neighboring  land  from 
reaching  it.*  Upon  the  slopes  themselves  should  be  made 
ditches,  called  "  Catch-water  drains,"  running  obliquely 
downwards,  to  receive  the  water  of  rains,  and  conduct  it 
into  the  side  ditches. 

The  side-slopes  may  be  advantageously  sown  with 
grass-seed.  The  roots  of  the  grass  will  bind  the  eartb 

»  giro  page  128  t  Gayffier,  p.  162 


BLASTING.  161 

together,  and  prevent  its  slipping.  A  overing  of  3  or  4 
inches  of  good  soil  should  be  previous  7  spread  over  the 
side-slopes,  but  if  they  are  steeper  than  If  to  1,  the  soil 
will  not  lie  upon  them.  They  may  also  be  sodded  ;  the 
sods  being  laid  on,  either  with  the  grass  side  uppermost, 
or  edgewise,  with  their  faces  at  right  angles  to  the  slope. 
The  latter,  "  Edge-sodding,"  is  the  most  efficient,  but 
most  expensive. 

TUNNELING. 

When  the  excavation  exceeds  a  certain  depth,  it  will 
be  cheaper  to  make  a  tunnel  as  a  substitute.  The  amount 
of  excavation  will  be  much  less,  but  the  cost  of  each  yard 
of  it  will  be  much  greater.  Calculation  in  each  case 
can  alone  decide  at  what  depth  it  would  be  economical  to 
abandon  the  open  excavation,  and  to  commence  the  tun- 
nel. Sixty  feet  is  an  approximate  limit  in  ordinary  earth. 
The  necessity  for  tunnels  seldom  occurs,  however,  in  the 
construction  of  common  roads,  though  frequent  in  the 
great  roads  of  the  Alps,  and  on  railroads  ;  in  the  chapter 
devoted  to  which  they  will  therefore  be  more  fully  noticed. 


BLASTING. 


Not  only  rock,  but  frozen  earth,  and  sometimes  very 
compact  clay,  are  removed  by  blasting  with  powder. 
The  holes  are  drilled  by  a  long  iron  bar  of  the  hardest 
steel,  chisel-edged,  which  is  raised  and  let  fall  on  the  de- 
sired point,  and  at  each  stroke  turned  partially  around,  so 
that  the  cuts  cross  each  other  like  the  rays  of  a  star  *. 
The  holes  are  made  from  1  to  3  inches  in  diameter,  and 
from  1  to  4  feet  deep.  One  man  can  drill  in  a  day  18 
inches,  of  one  3  inches  in  diameter,  in  rock  of  average 
hardness.  When  water  percolates  nto  the  hole,  it  must 


162          THE  CONSTRUCTION  OF  ROADS. 

be  dried  with  oakum  and  quicklime,  and  the  powder  en- 
closed in  a  water-proof  cartridge.  The  proper  proportion 
of  powder  being  introduced  by  a  funnel  and  copper  tube, 
(so  that  none  may  adhere  to  the  side)  a  wadding,  of  hay, 
moss,  or  dry  turf,  is  placed  upon  it,  and  the  remainder  of 
the  hole  is  filled  with  some  packing  material.  This  is 
usually  sand,  but  by  far  the  best,  for  safety  and  efficiency, 
is  dried  clay,  rolled  into  balls  or  cylinders,  and  dried  at  a 
smith's  forge,  as  much  as  can  be,  without  its  falling  to 
pieces.  The  next  best  material  is  the  chippings  and  dust 
of  broken  brick,  moistened  slightly  while  being  rammed. 
An  inch  or  two  of  the  wadding  being  simply  pressed 
down  upon  the  powder,  the  filling  material  is  rammed,  or 
"  tamped,"  with  a  copper  wire,  till  it  becomes  very  com- 
pact. Through  it  passes,  from  the  powder  to  the  surface, 
some  means  of  ignition.  A  straw,  filled  with  priming 
powder,  and  ignited  by  a  slow  match,  was  formerly 
employed  for  this  purpose.  But  of  late  years  this  has 
been  generally,  and  should  be  universally,  superseded  by 
the  safety-fuse.  This  has  the  appearance  of  a  common 
tarred  rope,  and  is  so  prepared  that  the  length  of  it,  which 
will  burn  any  given  time,  can  be  exactly  known,  so  that 
no  premature  explosion  need  be  feared. 

The  proper  charge  of  powder,  and  the  direction  of  the 
holes,  are  very  important,  both  for  efficiency  and  econo- 
my. The  usual  charge  is  one-third  of  the  depth  of  the 
hole  ;  but  such  a  rule  is  evidently  irrational,  for  the 
amount  of  a  charge  so  proportioned  will  vary  with  the 
bore.  The  proper  regulator  of  the  charge  is  the  length 
of  "  the  line  of  least  resistance"  i.  e.  the  shortest  dis 
tance  from  thp  bulk  of  the  powder  to  the  outside  of  the 
rock.  Thus  in  the  figure,  AB  being  the  hole  bored,  and 
B  the  powder,  BC  is  the  "  line  of  least  resistance,' 


BLASTING. 


which  should  not  be  in  the  direction 
of  the  hole  bored.  The  proper  charge 
depends  on  it,  and  not  at  all  on  the 
depth  AB.  To  produce  similar  pro- 
portional results  in  different  blasts, 
the  charges  must  be  as  the  cubes  of 
the  respective  lines  of  least  resist- 
ance. Thus,  if  four  ounces  of  pow- 
der will  just  suffice  to  blast  a  solid  rock  in  which  BC  is 
2  feet,  the  charge  for  another  in  which  BC  was  3  feet, 
would  be  given  by  the  proportion  23 :  4  :  :  33 :  13£  ounces. 
On  these  data  the  following  table  is  formed.* 


Line  of  least 
resistance. 

Charges  of 
powder. 

Line  of  least 
resistance. 

Charges  of 
powder. 

Feet,  inches. 

Lbs.  Oz. 

Feet.  Inches. 

Lbs.  Oz. 

1        0 

0       Ok 

4 

2      0 

1       6 

0        l| 

4       6 

2   131 

2       0 

0     4 

5 

3   141 

2       6 

0     7£ 

6 

6  12" 

3       0 

0  131 

7 

10  111 

3       6 

1     5i 

8 

16     0 

The  following  table  will  also  be  found  very  convenient 


Diameter  of 
the  hole. 

Powder  in  one 
inch  of  hole. 

Powder  in  one 
foot  of  hole. 

Depth  of  hole  to  contain, 
one  Ib.  of  powder. 

Inches. 

Lbs.    Oz. 

Lbs.      Oz. 

Inches. 

1 

0     0.419 

0     5.028 

38.197 

H 

0     0.942 

0  11.304 

16.976 

2 

0     1.676 

1     4.112 

9.549 

2| 

0     2.618 

1   15.416 

6.112 

3 

0     3.770 

2  13.240 

4.244 

*  London  Mechanics'  Magazine,  xxxiii.-  597,  Dec   1840  ;  and  profes* 
sona!  papers  of  Royal  Military  Enjnneers,  vol.  4 


164 


THE    CONSTRUCTION    OF    ROADS. 


When  the  rock  is  stratified,  Fis-  "• 

having  beds  and  seams,  as  in 
the  figure,  holes  bored  paral- 
lel to  the  joints  will  produce 
much  greater  effect  than  the 
usual  vertical  ones. 

When  a  rocky  surface  is  to  '\A\\\\\\\\\\\ 

he  cut  down  to  a  line  AB,  the  holes  should  be  oblique,  as 

Fig.  78. 


in  the  figure.  In  some  cases,  a  horizontal  one,  from  B 
towards  A  would  be  advantageous. 

On  a  high  face  of  rock  a  system  of  undermining  may 
be  usefully  employed,  by  blowing  out  a  mass  below,  and 
removing  the  remaining  overhanging  portion  by  crowbars, 
wedges,  &c. 

The  crater,  or  cavity  formed  by  an  explosion,  is  as- 
sumed to  be  a  truncated  cone,  which  has  its  inner  or  smaller 
diameter  equal  to  half  the  diameter  of  the  mouth  of  the 
crater.  It  has  been  found  by  experiment  that  the  outer 
diameter  of  the  crater  may  be  increased,  in  ordinary  soils, 
by  excessive  charges,  to  three  times  the  length  of  the 
*'  line  of  least  resistance,"  but  not  much  beyond  this  ;  and 
that  within  this  limit  this  diameter  increases  nearly  in  the 
ratio  of  the  square  root  of  the  charge. 

The  most  unfavorable  situation  for  a  charge  is  where  a 
re-entering  angle  is  to  be  blown  out,  as  the  rock  all  around 
it  exerts  a  powerful  resisting  pressure.  The  charge  needs 


EMBANKMENTS.  165 

to  be  proportionally  increased.  This  case  constantly  oc- 
curs in  blasting  out  narrow  passages. 

No  loud  report  should  be  heard,  nor  stones  be  thrown 
out.  The  best  effect  is  produced  when  the  report  is 
trifling,  but  when  the  mass  is  lifted,  and  thoroughly  frac- 
tured, without  the  projection  of  fragments.  If  the  rock 
be  only  shaken  by  a  blast,  and  not  moved  outwardly,  a 
second  charge  in  the  same  hole  will  be  very  effective. 

Any  kind  of  compact  brush,  such  as  pine  or  cedar 
boughs,  laid  on  rocks  about  to  be  blasted,  will  almost 
completely  prevent  the  flying  of  fragments,,  and  thus  les- 
sen the  danger  to  persons  and  buildings  in  the  vicinity. 

The  safety  of  blasting  operations  may  be  greatly  in- 
creased by  applying  galvanism  to  the  ignition  of  the 
powder,  which  can  then  be  effected  at  any  distance. 
By  its  aid  a  row  of  blasts  can  be  exploded  simultaneously, 
by  which  their  effective  power  is  greatly  increased.  In 
this  way,  a  single  blast,  of  nine  tons  of  powder,  contained 
in  three  cells,  removed  one  million  tons  of  rock  from  a 
cliff  at  Dover,  with  a  saving  of  $50,000 

EMBANKMENTS. 

Perfect  solidity  is  the  great  desideratum  in  anificial 
road-making.  Every  precaution  must  therefore  be  em- 
ployed, in  forming  a  high  bank,  to  lessen  its  tendency  to 
slip.  From  the  space  which  the  bank  is  to  occupy,  all 
vegetable  or  perishable  matter,  and  all  porous  earth  and 
loose  stones,  should  be  removed.  On  this  space  the 
earth  is  then  deposited,  to  form  the  embankment,  which 
is  usually  made  of  full  height  at  its  commencement,  and 
is  extended  by  "  tipping"  earth  from  the  extremity,  and 
so  carried  out  on  a  level  with  the  top  surface.  But  an 
embankment  thus  formed  will  be  deficient  in  compact 


166  THE   CONSTRUCTION    OF    ROADS 

ness ;  for  the  particles  of  earth,  which  are  emptied  from 
the  top  of  the  bank,  will  temporarily  stop  in  their  descent 
at  the  point  of  the  slope  at  which  the  friction  becomes 
sufficient  to  balance  their  gravity  ;  and  when  more  earlh 
comes  upon  them,  they  will  give  way  and  slide  lower 
down,  causing  the  portions  above  them  to  slip  and  crack, 
and  thus  delaying  for  a  long  time  the  complete  consoli- 
dation. 

This  method  is,  however,  cheap  and  rapid.  Its  rapid- 
ity will  be  increased  by  obtaining  more  "  tipping  places," 
which  can  be  effected  by  forming  the  bank  at  first  wider 

Fig.  79. 


b        B 

at  top,  and  narrower  at  bottom,  than  it  is  finally  to  be, 
(i.  e.  forming  abed  instead  of  ABCD)  and  subsequently 
throwing  down  the  superfluous  earth  from  the  top  to  give 
the  proper  width  at  bottom.* 

The  solidity  of  embankments,  which  are  made  by 
tipping  from  the  ends  may  be  increased  by  forming  the 
outside  portions  of  the  bank  first,  and  gradually  filling  up 
towards  the  middle,  so  that  the  earth  may  arrange  itself 
with  a  tendency  to  move  towards  the  centre,  if  at  all.t 

To  ensure  the  stability  of  embankments,  they  should, 
however,  be  formed  by  depositing  the  earth  in  successive 
layers  or  courses,  not  more  than  three  or  four  feet  thick  ; 
and  the  vehicles,  conveying  the  materials,  should  be  re- 
ft Laws  of  Excavation  and  Embankment  on  Railways,  p.  59 
t  Mahan,  p.  287. 


EMBANKMENTS. 


167 


quired  to  pass  over  the  bank  at  each  trip,  so  as  to  com- 
press the  earth.  If  the  case  warranted  the  expense,  each 
course  might  with  advantage  be  well  rammed.  To  les 
sen  the  danger  of  slips,  the  layers  should  be  made  some- 
Fig. 


what  concave,  as  in  Fig.  80.     If  made  convex,  as  in  the 
next  figure,  and  as  they  are  apt  to  become,  in  the  most 

Fig.  81. 


natural  mode  of  forming  them,  portions  would  tend  to 
slip  off  in  the  direction  of  the  layers,  while  the  arrange- 
ment of  concave  layers  would  resist,  instead  of  assisting, 
any  slip.  A  framework  of  timber  has  sometimes  been 
inserted  in  a  bank  to  bind  it  more  firmly  together. 

An  embankment  should  always  be  formed  at  first  of  its 
full  width,  and  not,  from  a  mistaken  economy,  be  at  first 
made  narrow,  to  be  subsequently  increased  by  lateral  ad- 
ditions ;  for  the  new  portion  will  never  unite  perfectly 
with  the  old. 

At  the  foot,  or  "  toe,"  of  the  bank,  a  slight  excavation 
may  be  made  to  resist  its  tendency  to  spread,  or  a  low 
but.  massive  stone  wall  may  be  there  erected. 

The  slopes,  like  those  of  excavations,  should  be  grassed, 
or  sodded.  If  exposed  to  the  action  of  water,  a  row 
of  planks,  grooved  and  tongued,  and  sharpened  at  bottom, 


(68  THE    CONSTRUCTION    OF    ROADS. 

should  be  driven  at  their  foot,  forming  a  "  sheet-piling  ,  * 
and  the  slopes  themselves  should  be  protected  with  a 
"  slope-wall"  composed  of  rough  stones,  from  one  to  two 
feet  thick,  laid  without  mortar,  with  their  faces  at  right 
angles  to  the  slope,  and  "  breaking  joints"  as  perfectly  as 
possible.  To  prevent  their  being  tin  own  out  of  place  by 
the  swelling  and  heaving,  which  is  caused  by  the  freezing 
of  the  rain-water  retained  by  the  clayey  material  of 
which  an  embankment  may  be  composed,  a  layer,  one  or 
two  feet  thick,  of  coarse  gravel,  should  be  placed  on  the 
slope  before  laying  the  stone  facing,  so  that  the  rain-wa- 
ter can  at  once  pass  through  this  porous  coating.  At  the 
foot  of  the  slope,  an  "apron,"  or  mass  of  loose  stoms 
may  be  deposited. 

SWAMPS    AND    BOGS. 

When  an  embankment  is  to  be  made  through  a  swamp 
bog,  marsh,  or  morass,  many  precautions  are  necessary. 

If  the  bog  be  less  than  four  feet  deep,  and  have  a 
solid  bottom,  all  the  soft  matter  should  be  removed,  and 
an  embankment  raised  upon  the  hard  bottom. 

If  it  be  deeper,  but  not  very  soft,  the  surface  may  be 
covered  with  two  rows  of  swarded  turf;  the  lower  being 
laid  with  its  grassy  face  downward,  the  other  with  that 
face  upward,  and  the  embankment  raised  upon  them. 

When  the  swamp  is  deep  and  fluid,  thorough  draining 
is  the  first  and  most  important  point.  On  each  side  of 
the  road,  wide  and  deep  ditches  must  be  cut,  to  collect 
the  surface  water,  and  to  carry  it  off  into  the  natural  wa- 
ter-courses. Numerous  smaller  ditches  must  be  cut,  at 
short  intervals,  across  the  road-way,  from  one  main  drain 
to  the  other,  descending  both  ways  from  the  centre.  This 
operation  will  consolidate  the  surface  between  the  main 


SIDE-HILL    ROADS.  169 

ditches.  The  cross-drains  may  be  filled  with  broken 
stones,  (or  bushes,  if  they  will  always  remain  under  wa- 
ter, as  otherwise  they  will  decay,  and  cause  the  road  to 
sink)  and  on  this  foundation  the  embankment  maybe  raised. 
In  extreme  cases,  the  lower  portions  of  the  embank- 
ment must  be  formed  of  brush-wood,  arranged  in  fascines 
which  are  a  specific  remedy  against  water.  They  are 
formed  by  carefully  selecting  the  long,  straight,  and  slen- 
der branches  of  underwood,  and  tying  them  up  in  bundles, 
from  9  to  12  inches  in  diameter,  and  from  10  to  20  feet 
long.  A  layer  of  these  fascines  is  laid  across  the  road  ; 
a  second  layer  in  the  direction  of  the  road  ;  and  so  on,  to 
as  great  a  thickness  as  may  be  required  to  raise  the  road- 
bed perfectly  high  and  dry.  Sharp  stakes  are  driven  at 
intervals  to  fasten  together  the  layers.  Poles,  or  young 
trees,  may  be  laid  across  every  other  course.  Upon  this 
platform  of  fascines  may  be  laid  large  flat  stones,  and  upon 
them  a  course  of  earth  and  gravel. 

SIDE-HILL    ROADS. 

When  a  road  runs  along  the  side  of  a  hill,  it  will  be 
most  cheaply  formed,  by  making  it  half  in  excavation  and 
half  in  embankment.  But  as  the  embankment  would  be 


Fig.  82. 


170         THE  CONSTRUCTION  OF  ROADS. 

liable  to  slip,  if  simply  deposited  on  the  natural  surface  of 
the  ground,  the  latter  should  be  notched  into  steps,  or  off 
sets,  in  order  to  retain  the  earth.  In  adjusting  the  height 
of  the  made  ground,  an  allowance  should  be  made  for  its 
subsequent  settling. 

If  the  surface  be  very  much  inclined,  both  the  cuttings 
and  fillings  will  need  to  be  supported  by  "retaining  walls," 


Fig.  83. 


which  may  be  laid  dry  if  composed  of  large  stones,  or 
in  mortar.  The  proper  thickness  which  should  be  given 
to  them,  will  be  investigated  under  the  head  of  "  Me- 
chanical structures." 

.  If  the  side  hill  be  of  rock,  the  steep  slope  at  which  that 
material  may  safely  be  cut,  will  enable  the  upper  wall  to 
be  dispensed  with. 

When  the  road  is  required  to  pass  along  the  face  of  a 
nearly  perpendicular  precipice,  at  a  considerable  height, 
(a  case  which  sometimes  occurs  in  passing  a  projecting 
point  of  the  rocky  bank  of  i  river  in  a  mountainous  dis- 


TRIMMING    AND    SHAPING. 


171 


.  84. 


tnct)  it  may  rest  on  a  frame-work 
formed  of  horizontal  beams,  deep- 
ly let  into  the  face  of  the  preci- 
pice, and  supported  at  their  outer 
ends  by  oblique  timbers,  the  low- 
er ends  of  which  rest  in  notches 
formed  in  the  rock. 

TRIMMING    AND    SHAPING. 


To  form  the  side-slopes  with 
precision,  to  the  proper  inclina- 
tion, a  simple  bevel,  " 
or  "  clinometer,"  may  be 
ployed  with  great  advantage.  It  consists  of  two  strips  of 
board,  AB,  AC,  fastened  to  each  other  at  right  angles 
and  connected  by  a  third  Pi  gg 

one,  CB.  When  the  de- 
sired slope  is  2  to  1,  make 
AB  twice  the  length  of  AC. 
Place  C,  orB,  at  any  known 
point  of  the  slope ;  make 
AC  vertical  by  the  plumb-line  ;  and  then  will  BC  com 
cide  with  the  slope  desired. 

Another  implement  for  the  same  purpose  is  formed  of 
a  single  strip  of  wood,  to  which  is  attached  a  triangle 

Fig.  86. 


172  THE  CONSTRUCTION  OF  ROADS. 

with  base  and  height  corresponding  to  those  of  the  de- 
sired slope.  When  a  spirit-level,  resting  upon  the  top  of 
this  triangle,  is  horizontal,  the  inclined  strip  will  coincide 
with  the  slope  sought. 

A  more  general  "  Clinometer"  is  shown  in  the  accom- 
panying figure.     It  consists  of  a  spirit-level,  moveable  on 

Fig.  87 


a  pivot,  which  is  the  centre  of  a  quadrant  divided  into  de- 
grees. To  measure  a  slope,  place  the  bar  upon  it,  and 
turn  the  level  till  the  bubble  is  in  its  centre.  The  read- 
ing at  the  top  of  the  level  will  indicate  the  inclination  of 
the  slope.  To  increase  its  portability,  the  long  bar 
doubles  up  on  a  hinge  in  its  middle.* 

To  shape  the  tops  of  the  embankments,  and  the  bot- 
toms of  the  cuttings,  in  accordance  with  the  desired  pro- 
file of  the  road,  attach,  to  the  under  side  of  a  common 

*  Simms  on  Levelling,  p  96 


MECHANICAL    STRUCTURES. 

Fig.  88 


173 


mason's  level,  a  triangle  ABC,  with  its  base  and  height 
so  proportioned  as  to  correspond  to  the  "  crowning"  of  the 
road  ;  1  in  24  for  example.  Or,  instead  of  the  triangle, 
gauges  of  different  lengths,  rnoveable  on  thumb-screws, 
maybe  made  to  project  below  the  level,  to  proper  depths.* 

2.  MECHANICAL  STRUCTURES. 

Under  this  head  are  included  the  bridges,  culverts,  and 
other  works  of  the  mason  and  carpenter,  which  are  re- 
quired for  the  purposes  of  the  road. 


The  most  simple  and  natural  form  of  a  bridge  consists 
of  two  timbers,  laid  across  the  stream,  or  opening,  which  is 
to  be  passed  over,  and  covered  with  plank  to  form  the 
road-way.  Walls  should  be  built  to  support  each  end  of 
the  timbers,  and  are  named  the  abutments.  The  width 
of  the  opening  which  they  cross  is  termed  the  stretch,  or 
bay.  The  timbers  themselves  are  the  string-pieces. 
Their  number  and  size  must  of  course  increase  with  the 
stretch.  For  a  stretch  of  16  feet,  they  should  be  about 

*  Parnell,  p.  261. 


174 


THE    CONSTRUCTION    OP   ROADS 


15  inches  deep  by  8  broad,  and  be  placed  at  intervals  ol 
about  2  feet.*  The  greatest  weight  which  can  come  upon 
them  is  when  the  surface  of  the  bridge  is  covered  with 
men  standing  side  by  side,  and  is  then  equal  to  120  Ibs.  per 
square  foot  of  surface,  independently  of  the  weight  of  the 
materials.  Recent  experiments  make  this  only  70  Ibs. 

This  simple  construction  is  only  applicable  to  short 
{stretches.  For  spaces  of  greater  width,  supports  from 
the  bottom  of  the  opening  may  be  placed  at  proper  inter- 
vals. They  may  be  piers  of  masonry,  or  upright  props  or 
shores  of  timber,  properly  braced,  and  supported  on  piles, 
if  the  foundation  be  insecure.  They  will  divide  the  long 

Fig.  89. 


stretch  into  a  number  of  shorter  ones,  and  support  the 
ends  of  the  timbers  by  which  each  of  them  is  spanned. 

But  if  the  opening  be  deep,  or  occupied  by  a  rapid 
stream,  it  is  very  desirable  to  avoid  the  use  of  any  such 
obstructions.  Means  must  therefore  be  devised  for 
strengthening  the  beams,  so  as  to  enable  them  to  span 
larger  openings.  This  may  be  effected  by  supports  from 
below,  or  from  above. 

Of  supports  from  below,  the  simplest  are  shorter  tim 
pers,  (bolsters,  or  corbels)  placed  under  the  main  ones 

*  Tredgold's  Carpenf  y,  p.  148.  This  gives  a  great  surplv  s  of  strength. 


BRIDGES.  175 

to  which  they  are  Fiff-  9°- 

firmly  bolted,  and  j  f~ 

projecting      about    "•  ^|| 

one-third    of    the  4                                      If 

stretch.    This  will  4                                   j^ 

considerably       in-  * 

crease  the  stiffness. 

Still  more  effective   are   oblique  braces,  or  "  struts," 
supporting  the  middle  of  the  beam,  and  resting,  at  their 

Fig.  91 


lower  ends,  in  "  shoulders,"  cut  into  the  abutments.    Sim- 
ilar braces  may  be  applied  to  the  "  bolsters"  of  Fig.  90. 
As  the  span  increased,  these  braces  would  become  sc 

Fig.  92. 


oblique  as  to  lose  much  of  their  efficiency.  A  straining- 
piece  is  therefore  interposed  between  them.  Thirty-five 
feet  may  thus  be  spanned. 

For  longer  stretches,  the  bolsters,  braces,  and  straining- 
beams  may  be  combined,  as  in  Fig.  93.     The  principle  ol 
this  method  may  be  extended  to  very  wide  openings. 
12 


176         THE  CONSTRUCTION  OF  ROADS. 
Fig.  93. 


But  in  many  cases  supports  from  below  may  be  objec 
tionable,  as  exerting  too  much  thrust  against  the  abut 
ments,  and  being  liable  to  be  carried  away  by  freshets, 
&c.  The  beams  must  in  such  cases  be  strengthened  by 
supports  from  above 

The  simplest  form  of  such  is  shown  in  Fig.  94,  m 
which  the  horizontal  beam  is  supported  by  an  upright 

Fig.  94. 


"king-post,"  to  which  it  is  attached  by  an  iron  strap, 
as  in  the  figure,  or  by  the  upright  "  king-post"  being 
formed  of  two  pieces,  bolted  together,  and  enclosing  the 
beam  between  them.  The  king-post  itself  is  supported 
by  the  oblique  braces,  or  "  struts,"  which  rest  against 
notches  in  the  horizontal  beam. 

Since   ;he  king-post  acts  as  a  suspending  tie,  an  iron 


BRIDGES. 
Fig.  95. 


177 


red  may  be  advantageously  substituted  for  it.  The  oblique 
braces  may  be  also  stiffened  by  iron  ties,  binding  them  to 
the  main  timbers,  as  in  Fig.  95. 

For  longer  stretches,  a  straining  beam  may  be  intro- 

Fig.  96. 


duced  between  the   struts,  as  in  Fig.  96,  in  which  the 
posts  are  represented  as  enclosing  the  beam. 

For  bridges  of  greater  span,  and  more  complicated 
structure,  the  professional  assistance  of  a  civil  engineer 
should  be  secured.  On  bridges,  see  Appendix  F.  For 
data  and  formulas  for  calculating  the  strength  of  beams 
and  trusses,  see  Gillespie's  "  Strength  of  Materials  and 
Stability  of  Structures." 


178 


THE  CONSTRUCTION  OF  ROADS. 


CULVERTS  AND  DRAINS. 

These  structures  are  necessary  for  carrying  under  a 
road  the  streams  which  it  intersects.  They  are  also  need- 
ed to  carry  the  waters  of  the  ditches,  from  the  upper  side 
of  a  road,  to  that  side  on  which  lie  the  natural  water 
courses  into  which  they  must  finally  be  discharged  Theii 
simplest  form  consists  of  two  walls  of  stone  or  brick 
covered  with  slabs,  and  having  a  foundation,  either  ol 
wood  (if  always  wet)  or  of  stone,  laid  in  the  form  of  an 
inverted  arch,  as  shown  in  Fig.  97. 

cross-section  in  Figure  97. 
Their  size  must  be  propor- 
tioned to  the  greatest  quantity 
of  water  which  they  can  ever 
be  required  to  pass,  and  should 
be  at  least  18  inches  square, 
or  large  enough  to  admit  a  boy 
to  enter  to  clean  them  out.  Their  bottoms  should  be  in- 
clined 1  in  120,  or  1  inch  in  10  feet.  When  the  road 
slopes,  the  inclination  of  the  culvert  may  be  increased,  if 
necessary,  by  making  it  cross  the  road  obliquely.  At 
each  end  flat  stones  should  be  sunk  vertically,  or  sheet- 
piling  driven,  to  guard  against  the  undermining  effects  of 
the  water.  The  length  of  a  culvert  under  an  embank- 
ment will  be  equal  to  the  width  of  the  road,  increased  by 
the  distance  on  each  side,  to  which  the  slopes  run  out,  at 
the  depth  at  which  the  culvert  is  placed.  At  each  end  of 
it  should  be  built  wing-walls,  their  tops  having  an  outward 
and  downward  slope  corresponding  to  that  of  the  embank- 
ment. Their  ground  plan  may  be  rectangular,  trapezoi- 
dal, or  curved. 

In  districts  where  stone  is  scarce,  a  small  culvert  may 


CULVERTS    AND    DRAINS. 


179 


be  constructed  with  four  ranges  of  slabs  ;  *%.  98. 

grooves  being  cut  in  the  top  and  bottom 
slabs,  to  receive  the  upright  ones  which 
form  the  sides. 

A  cheap  culvert  may  be  built  of  brick, 
will)  a  semicircular  arch,  of  three  feet 
span  and  4  inches  thick.  F'g-  99. 

One  thousand  bricks  will 
build  26  running  feet.  If 
the  flow  of  water  be  small, 
the  bottom  may  be  merely 
covered  with  gravel,  over 
which  is  then  poured  grout  of  hydraulic  cement,  forming 
a  superficial  concrete. 

To  obtain  greater  strength,  the  Fi£- 10° 

arch  may  rest  on  abutments,  slo- 
ping inward,  and  the  bottom  of  the 
culvert  be  a  flat  inverted  arch. 

When  a  road  is  in  excavation, 
the  ditches  on  either  side  of  it 
will  sometimes  require  to  be  cov- 
ered, to  prevent  their  being  filled 
up  by  washings  from  the  sides. 
They  may  then  be  formed  as  in 
Fig.  97 ;  but  spaces  of  half  an  inch  in  width  should  be 
left  between  the  covering  stones.  A  layer  of  brushwood 
should  be  placed  over  these,  and  the  remainder  of  the 
ditch  filled  up  to  the  surface  with  broken  stones,  through 
which  the  water  can  filler.* 

Similar  but  smaller  drains  may  be  formed  at  intervals 
under  the  road,  diverging  from  its  centre  like  the  two 


»  Parnell,  p  95 


180          THE  CONSTRICTION  OF  ROADS. 

branches  of  the  letter  V>  a°d  descending  from  the  angu- 
lar point  to  the  side-ditches.  They  are  called  "  mitre 
drains."  In  very  wet  ground,  a  deep  but  narrow  drain, 
filled  with  broken  stones,  may  be  carried  through  the 
middle  of  the  road. 

CATCHWATERS,    OR  WATER-TABLES. 

These  are  very  shallow  paved  ditches,  formed  across 
the  road  upon  a  slope,  to  catch  the  water  which  runs 
down  its  .length,  (and  which  would  otherwise  furrow  up 
the  road-way)  and  to  turn  it  off  into  the  side-ditches. 
They  are  also  necessary  in  the  hollows  which  exist  at  the 
points  where  a  descent  and  ascent  meet.  They  should 
be  so  laid  that  a  carriage  will  not  feel  any  shock  in  pass- 
ing over  them.  Their  bottom  may  be  flat,  and  six  feet 
wide,  and  for  twelve  feet  on  each  side  they  may  rise  one 
inch  to  the  foot.  The  side-slope,  down  which  they  dis- 
charge their  waters,  should  be  also  paved.  Sometimes 
lor  economy  they  are  used  as  a  substitute  for  a  culvert  to 
carry  the  waters  of  a  small  stream  across  the  road  ;  but 
this  is  very  objectionable,  particularly  from  the  ledges  of 
ice  which  will  be  there  formed  in  winter.  They  are  some- 
times shaped  like  a  V>  with  the  point  directed  up  the  as- 
cent, and  will  then  divide  the  waters.  In  mountainous 
situations  they  should  be  located  obliquely  to  the  axis  of 
the  road,  and  the  most  advantageous  position  will  evident- 
ly be  that  which  has  the  greatest  descent  with  the  least 
length,  and  may  be  geometrically  determined. 

Let  the  longitudinal  slope  of  the  road  descending  from  A  to 
B,  be  771  to  1 ;  and  let  its  transverse  slope  from  A  to  C  be  n  to 
1 ;  the  former  being  here  supposed  steeper  than  the  lattet, 
It  is  required  to  determine  the  position  of  the  catchwater  AD 
so  that  it  may  have  the  greatest  slope  possible. 


CATCHWATERS. 


181 


Fig.  101. 


If  a  line,  BC,  be  so  drawn  on  the 
Burface  of  the  road  as  to  be  horizon- 
tal, the  desired  line  of  greatest  slope, 
AD,  will  be  perpendicular  to  it,  as  ex- 
plained on  page  75.  The  position  of 
this  horizontal  line  must  therefore  be 
first  determined.  The  two  points,  A 
and  B,  which  it  unites,  being  on  the 
same  level,  the  descent  from  A  to  B 
equals  that  from  A  to  C.  These  de- 
scents are  expressed  respectively  by 

AB        ,   AC 

-  and   -  ,  giving  the   equation,    ~ 

AB        AC  n 

-  =  —  ;  whence  AC  =  AB  •  —  . 
m  n  m 

Therefore,  to  obtain  the  position  AD  by  a  graphical  con« 
struction,  make  AB  of  any  length,  and  set  off  AC  (as  given  by 
the  equation)  at  right  angles  to  it;  join  CB,  and  from  A  draw 
the  perpendicular  AD,  which  will  be  the  line  required. 

If  it  be  required  to  define  the  position  AD,  by  the   angle 
BAD,  it  will  be  seen   that   BAD  =  ACB  ;    and  that 
A®  AB  AB 


-         - 
-- 


If  m  —  20  and  n  —  30,    sin.  ACB  =  .5555,  and  ACB  = 
33°  45'. 

Care  must  be  taken  to  avoid  placing  the  catchwater  in 
the  direction  of  the  diagonal  of  the  rectangle  formed  by 
the  four  wheels  of  a  carriage  ;  in  order  to  avoid  the  double 
shock  which  would  otherwise  be  caused  by  two  wheels 
sinking  into  it  at  onc<\ 

A  cheap  suustitute  for  a  catchwater  on  -i  steep  slope  is 
a  mound  of  earth,  crossing  the  road  obliquely.  This  will 


182 


THE    CONSTRUCTION    OF    ROADS. 


also  serve  as  a  ^^^^^^^  F'S- 102. 
resting-place  on 
the  ascent.  It 
should  be  so  pro- 
portioned, that 
carriages  may  pass  it  without  inconvenience. 

RETAINING    WALLS. 

Retaining,  sustaining,  revetment,  and  breast  walls,  as 
their  various  names  import,  are  employed  to  support 
masses  of  earth,  and  to  resist  their  lateral  pressure.  Their 
use,  when  a  road  passes  along  a  steep  hill-side,  has  been 
already  explained.  In  passing  through  villages  also,  where 
land  is  valuable,  a  narrower  space  will  suffice  for  a  road 
in  excavation  or  embankment,  if  retaining  walls  be  sub 
stituted  for  side-slopes. 

The  calculation  of  the  necessary  thickness  for  retain- 
ing walls,  to  enable  them  to  resist  the  thrust  of  the  earth 
which  they  are  intended  to  support,  is  a  problem  of  con- 
siderable intricacy  of  investigation,  as  well  as  one  of  much 
uncertainty,  in  consequence  of  the  numerous  and  greatly 
varied  data  required. 


Fig.  103. 


When  a  wall,  of 
which  ABCD  is  a 
transverse  section, 
supports  a  mass  of 
earth,  there  is  a 
certain  triangular 
portion,  ADE,  of 
the  earth,  which 
would  slide  down- 
ward if  the  wall 
were  removed,  and  which  therefore  now  presses  against 


RETAINING    WALLS.  183 

the  wall  with  a  force,  varying  with  its  height,  its  specific 
gravity,  and  the  angle,  ADE,  at  which  the  earth  would 
stand  if  unsupported.  The  wall  may  yield  to  its  pressure 
by  sliding  along  its  base,  or  along  some  horizontal  course, 
or  by  being  overturned  and  revolving  about  the  exterior 
edge  of  one  of  its  horizontal  joints.  The  latter  is  the 
only  danger  to  be  feared  in  a  well-built  wall. 

The  most  complete  investigation  of  the  problem  of  the  proper 
thickness  of  retaining  walls  has  been  made  by  M.  Poncelet  in 
a  Memoir,*  of  which  a  translation  has  appeared  in  the  Journal 
of  the  Franklin  Institute  for  1843.  It  contains  valuable  ta- 
bles as  well  as  formula.  Let  a  denote  the  angle  with  the  ver- 
tical made  by  the  line  of  the  natural  slope  of  the  earth,  and 
represented  by  ADE  in  the  figure.  It  will  vary  from  70°,  as 
in  the  case  of  very  fine  dry  sand,  to  35°,  as  in  the  case  ot 
heavy  clayey  earth.  Let  w  denote  the  weight  of  any  unit  of 
the  earth,  and  w'  that  of  the  same  unit  of  the  masonry.  The 
specific  gravity  of  the  former  ranges  between  1.4  and  1.9, 

and  that  of  the  latter  between  1.7  and  2.5. f     The  ratio  —  is 

w 

therefore  usually  between  f  and  1.  For  the  simplest  case, 
that  in  which  the  embankment  does  not  rise  above  the  wall,  the 
formula^  for  the  thickness  corresponding  to  any  height  H,  is 


Tan.  £  u  X  T8o  \/  —7  •  H. 

This  gives  a  stability  of  1.92  to  1,  or  nearly  double  that  of  a 
strict  equilibrium. 

For  the  usual  assumed  mean  values  of  a  =  45°,  and 
— -  =  f ,  the  formula  gives  for  the  required  thickness  of 
the  wall  TYo>  or  a  little  over  a  quarter  of  the  height. 


»  No.  13  du  Memorial  de  Tofficiet  du  Genie.  See  also  PHONY  ;  Re 
cherckes  sur  la  Poussee  des  Terres ;  aud  NAVIER  ;  Lefons  sur  VAppli 
tion  de  la  Mecanique  aux  Constructions. 

t  Navier.  t  Ponc»>let,  ^  12. 


184          THE  CONSTRUCTION  OF  ROADS. 

The  extreme  limits  in  any  case  are  from  TWV»  01  one- 
fifth  of  the  height,  with  compact  earth  and  heavy  mason- 
ry, to  rWirj  or  not  quite  half  the  height,  with  loose  earth 
and  light  masonry.*  The  precise  thickness  can  be  cal- 
culated by  the  preceding  formula  ;  after  noting  the  slope 
at  which  the  earth  naturally  stands,  and  weighing  a  cer- 
tain portion  of  the  masonry,  and  of  the  earth  previously 
thoroughly  moistened. 

When  there  is  an  embankment  rising  above  the  top  of 
the  wall,  the  proper  thickness  (in  cases  in  which  the  height 
of  the  superincumbent  load  does  not  much  exceed  the 
height  of  the  wall)  may  be  approximately  obtained  by 
substituting  in  the  same  formula,  instead  of  the  height 
of  the  wall,  the  sum  of  the  heights  of  the  wall  and  of  the 
earth  above  it.t 

Thus  far  both  faces  of  the  retaining  wall  have  been 
supposed  to  be  vertical.  But  the  same  strength  with  a 
less  amount  of  material  may  be  ob-  Fig.  104. 

tained  by  various  modifications  of  its 
section. 

The  face  of  the  wall  may  be  advan- 
tageously made  to  slope  with  a  "bdtir" 
varying  from  ^T,  or  £  inch  horizontal 
to  1  foot  vertical,  to  £,  or  2  inches  to  1 
foot. 

To  find  the  mean  thickness  of  such  a 
wall,  which  shall  have  the  same  stability 
as  another  wall  with  vertical  faces,  and 
of  the  thickness  obtained  by  the  preceding  rules,  subtract  from 
this  given  thickness  four-tenths  of  the  entire  projection  of  the 
bdtir.%  Thus,  if  the  given  thickness  be  4  feet,  and  the  height 
24  feet,  and  the  corresponding  mean  thickness  of  a  wall  with 


•  Poncelet,  §  34.  t  Ibid.  §  22  \  Ibid.  $  78. 


RETAINING  WALLS. 


185 


a  bdtir  ot  yV  be  desired,  it  will  be  4  .  —  T4ff Xff =4  .  —  .8=3.2. 
The  bdtir  is  supposed  not  to  exceed  one-fifth  of  the  height 
From  the  mean  thickness,  those  of  the  top  and  bottom  are 
readily  deduced,  knowing  the  height  and  bdtir. 

Fig.  105. 


The  desired  increase  of  thick- 
ness towards  the  bottom  of  a  wall 
is  often  given  by  offsets  at  its 
back.  Considerable  resistance  to 
the  overturning  of  the  wall  is  of- 
fered by  the  weight  of  the  earth 
which  rests  upon  these  offsets. 


Still  more  economical  of 
masonry  is  a  leaning  retain- 
ing wall,  in  which  the  back 
has  a  bdtir,  which  may  ad- 
vantageously be  1  in  6.  In 
this  case  strength  requires 
that  the  perpendicular  let  fall 
from  the  centre  of  gravity 
of  the  section  upon  the  base, 
should  fall  so  far  within  the 
inner  edge  of  the  base,  that 
the  stone  of  the  bottom  course  of  the  foundation  may 
present  sufficient  surface  to  bear  the  pressure  upon  it. 


»  Mahan,  p.  142. 


186         THE  CONSTRUCTION  OF  ROADS. 

The  strength  of  a  wall  may  be  still  farther  increased  by 
lessening  its  thickness,  and  employing  the  difference  of 
the  amount  of  masonry  in  buttresses  or  counter- forts,  at 
tached  to  its  back  at  regular  intervals,  and  firmly  banded 

Fig.  107. 


with  it.  The  trapezoidal  section  for  them  is  preferred,  as 
giving  a  broader  base  of  union.  Fig.  107  is  a  ground  plan 
of  such  an  arrangement. 

To  lessen  the  pressure  of  an  embankment,  that  portion 
of  it  next  the  wall  should  be  formed  in  compact  layers, 
inclining  downward  from  the  wall.  Through  the  wall 
should  be  left  holes  (barbacanes)  six  inches  high  and  three 
wide,  disposed,  in  the  quincunx  form,  at  distances  of  six 
feet  horizontally,  and  four  feet  vertically,  in  order  to  give 
vent  to  the  water  which  may  filtrate  through  the  bank. 

The  masonry  of  a  wall  which  has  to  sustain  great 
pressures,  requires  much  attention.  The  following  is 
part  of  the  specification  for  such  walls  of  rubble  ma- 
sonry on  the  public  works  of  the  state  of  New  York. 
"  The  stone  shall  be  sound,  well-shaped,  and  durable, 
and  of  not  less  than  6  inches  in  thickness,  and  three  feet 
area  of  bed.  The  smoothest  and  broadest  bed  shall  in 
all  cases  be  laid  down,  and  if  it  be  rough  and  uneven,  all 
projecting  points  shall  be  hammered  off;  and  the  same 
from  the  top  bed,  so  as  to  give  the  succeeding  stone  a 
firm  bearing.  In  all  cases  the  bed  shall  be  properly  pre- 
pared, by  levelling  up,  before  the  next  stone  is  laid,  but 


RETAINING  WALLS.  187 

no  levellers  shall  be  placed  under  a  stone  by  raising  it 
from  its  bed.  One-fourth  of  the  wall  shall  be  composed 
of  headers,  which  shall  extend  through  the  wall,  where 
it  is  not  more  than  two  feet  thick,  and  from  2  to  4  feet 
back  for  thicker  walls.  The  whole  shall  be  laid  in  hy- 
draulic mortar,  composed  of  the  best  quality  of  cement, 
and  clean  sharp  sand  ;  and  particular  care  shall  be  taken 
to  have  each  stone  surrounded  with  moif.ar,  and  tho- 
roughly bedded  ir  it." 


188  IMPROVEMENT    OF    THE    SURFACE 


CHAPTER  IV. 

IMPROVEMENT  OF  THE  SURFACE. 

"  Next  to  the  general  influence  of  the  seasons,  there  is  perhaps  no  cir- 
cumstance more  interesting  to  men  in  a  civilized  state,  than  ihe  perfection 
of  the  means  of  interior  communication." 

Committee  of  House  of  Commons,  1819. 

THE  surface  of  a  newly-made  road  is  generally  very 
deficient  in  the  important  qualities  of  hardness  and  smooth 
ness,  and  to  secure  these  attributes  in  their  highest  at 
tainable  degree,  it  is  necessary  to  cover  the  earth,  which 
forms  the  natural  surface  of  the  road,  with  some  other 
material,  such  as  stone,  wood,  &c.  The  benefits  of  such 
a  process  are  twofold,  consisting, 

1.  In  substituting  a  hard  and  smooth  surface  for  the 
soft  and  uneven  earth  ; 

2.  In  protecting  the  ground  beneath  it  from  the  action 
of  the  rain-water,  which,  by  penetrating  to  it,  and  remain 
ing  upon  it,  would  not  only  impede  the  progress  of  vehi 
cles,  but  render  the  road  too  weak  to  bear  their  weight. 

Such  a  covering  should  be  regarded,  not  as  an  arch  to 
bear  the  weight  of  the  vehicles,  but  simply  as  a  roof,  to 
protect  the  earth  beneath  it  from  the  weather ;  not  as  a 
substitute  for  the  soil  under  it,  but  only  as  a  protection  to 
that  soil  to  enable  it  to  retain  its  natural  strength.  Erro- 
neous views  on  this  point  have  caused  very  prejudicial 
practices,  particularly  in  the  case  of  broken  stone,  or 
McAdam-roads. 


EARTH    .ROADS.  189 

The  various  surfaces  will  be  considered  in  the  following 
order  ;  beginning  with  the  most  imperfect,  that  of  the 
unimproved  earth,  and  ending  with  the  most  perfect  yet 
attained — that  of  Railroads. 

1.  EARTH  ROADS. 

2.  GRAVEL  ROADS. 

3.  BROKEN  STONE,  OR  McADAM  ROADS. 

4.  PAVED  ROADS. 

5.  ROADS  OF  WOOD. 

6.  ROADS  OF  OTHER  MATERIALS. 

7.  ROADS  WITH  TRACKWAYS.   • 


1.  EARTH  ROADS. 

Roads  of  earth,  with  the  surfaces  of  the  excavations 
and  embankment  unimproved  by  art,  are  very  deficient  at 
all  times  in  the  important  requisites  of  smoothness  and 
hardness,  and  in  the  spring  are  almost  impassable.  But 
with  all  their  faults,  they  are  almost  the  only  roads  in  this 
country,  (the  scantiness  of  labor  and  capital  as  yet  pre- 
venting the  adoption  of  better  ones)  and  therefore  no  pains 
should  be  spared  to  render  them  as  good  as  their  nature 
will  permit. 

The  faults  of  surface  being  so  great,  it  is  especially  ne- 
cessary to  lessen  all  other  defects,  and  to  make  the  road  in 
all  other  respects  as  nearly  as  possible  "  what  it  ought  to 
be."  Its  grades  should  therefore  be  made,  if  possible,  as 
easy  as  1  in  30,*  by  winding  around  the  hills,  or  by  cut- 
ting them  down  and  filling  up  the  valleys.  Its  shape 
should  be  properly  formed  with  a  slope  of  1  in  20f  each 

»  See  page  41.  t  Page  51 


190         IMPROVEMENT  OF  THE  SURFACE. 

way  from  the  centre.  Its  drainage  should  be  made  very 
thorough,  by  deep  and  capacious  ditches,  sloping  not  less 
than  1  in  125,*  in  accordance  with  the  minimum  road 
slope.  Drainage  alone  will  often  change  a  bad  road  to  a 
good  one,  and  without  it  no  permanent  improvement  can 
be  effected.  Trees  should  be  removed  from  the  borders  of 
the  road,  as  intercepting  the  sun  and  wind  from  its  surface. 

If  the  soil  be  a  loose  sand,  a  coating  of  six  inches  of 
clay  carted  upon  it,  will  be  the  most  effective  and  the 
cheapest  way  of  improving  it,  if  the  clay  can  be  obtained 
within  a  moderate  distance.  Only  one-half  the  width 
need  be  covered  with  the  clay,  thus  forming  a  road  for  the 
summer  travel,  leaving  the  other  sandy  portion  untouched, 
to  serve  for  the  travel  in  the  rainy  season. 

If  the  soil  be  an  adhesive  clay,  the  application  of  sand 
in  a  similar  manner  will  produce  equally  beneficial  results. 
On  a  steep  hill  these  improvements  will  be  particularly 
valuable. 

When  the  road  is  worn  down  into  hollows,  and  requires 
a  supply  of  new  material,  its  selection  should  be  made 
with  great  care,  so  that  it  may  be  as  gravelly  as  possible, 
and  entirely  free  from  vegetable  earth,  muck,  or  mould 
No  sod  or  turf  should  ever  be  allowed  to  come  upon  the 
road,  to  fill  a  hole  or  rut,  or  in  any  other  way  ;  for,  though 
at  first  deceptively  tough,  they  soon  decay,  and  form  the 
softest  mud.  Nor  should  the  roadmakerrun  into  the  other 
extreme,  and  fill  up  the  ruts  and  holes  with  stones,  which 
will  not  wear  uniformly  with  the  rest  of  the  road,  but  will 
produce  hard  bumps  and  ridges.  The  plough  and  the 
scraper  should  never  be  used  in  repairing  a  road.  Their 
work  is  large  in  quantity,  but  very  bad  in  quality.  The 

•See  page  54 


EARTH    ROADS.  191 

plough  breaks  up  the  compact  surface,  which  time  and 
travel  had  made  tolerable ;  and  the  scraper  drags  upon 
the  road  from  the  side  ditches  the  soft  and  alluvial  matter 
which  the  rains  had  removed,  but  which  this  implement 
obstinately  returns  to  the  road. 

A  very  good  substitute  for  the  scraper,  in  levelling  the 
surface  of  the  road,  clearing  it  of  stones,  and  filling  up 
the  ruts,  consists  of  a  stick  of  timber,  shod  with  iron,  and 
attached  to  its  tongue  or  neap  obliquely,  so  that  it  is  drawn 
over  the  road  "  quartering,"  and  throws  all  obstructions 
to  one  side.  The  stick  may  be  six  feet  long,  a  foot  wide, 
and  six  inches  thick,  and  have  secured  to  its  front  side  a 
bar  of.  iron  descending  half  an  inch  below  the  wood. 

Every  hole  or  rut  in  a  road  should  be  at  once  filled  up 
with  good  materials,  for  the  wheels  fall  into  them  like 
hammers,  deepening  them  at  each  stroke,  and  thus  in- 
creasing the  destructive  effect  of  the  next  wheel. 

EFFECT    OF    WHEELS    ON    TH»   SURFACE. 

The  effects  of  broad  and  narrow  wheels  upon  roads 
have  been  much  discussed,  and  many  laws  enacted  to 
encourage  the  use  of  the  former.  Upon  a  hard  and  well- 
made  road,  (such  as  one  of  broken  stone)  there  is  little 
difference  between  them,  but  on  a  common  earth  road, 
narrow  wheels,  supporting  heavy  weights,  exercise  a  very 
destructive  cutting  and  ploughing  action.  This  dimin- 
ishes as  the  width  of  the  felloe  increases,  which  it  may 
do  to  such  an  extent,  that  the  wheel  acts  as  a  roller  in  im- 
proving, instead  of  injuring,  the  surface.  For  these  rea 
sons  the  New  York  turnpike  law  enacts  that  carriages, 
having  wheels  of  which  the  tire  or  track  is  six  inches 
wide,  shall  pay  only  half  the  usual  tolls;  those  with 
wheels  nine  inches  wide,  only  one-fourth  ;  and  that  those 
13 


il)2        IMPROVEMENT  OF  THE  SURFACE. 

with  twelve  inches  shall  pay  none  at  all.  The  proportions 
agree  precisely  with  those  deduced  from  observation  by 
an  experienced  English  roadmaker.*  The  felloe  should 
have  a  flat  bearing  surface  and  not  a  rounded  one.  The 
benefits  of  broad  wheels  are  sometimes  destroyed  by  over- 
loading them.  To  prevent  this,  when  tolls  are  collected, 
they  should  be  increased,  for  each  additional  horse,  more 
rapidly  than  the  direct  proportion  ;  thus,  if  one  horse  paid 
5  cents,  two  should  pay  1 1,  three  17,  &c.  Narrow  wheels 
are  particularly  injurious  when  in  rapid  motion,  for  having 
less  resistance  and  greater  velocity  than  others,  they  re- 
volve less  perfectly,  and  drag  more,  thus  producing  the 
worst  sort  of  effect.  Conical  wheels,  of  which  the  inner 
is  greater  than  the  outer  circumference,  tend  to  move  in 
a  curve,  and  being  forced  to  proceed  in  a  right  line,  exert 
a  peculiarly  destructive  grinding  action  on  the  road.  On 
McAdam  roads,  horses'  feet  exercise  a  more  destructive 
effect  than  the  wheels  of  vehicles.  It  has  been  calcula- 
ted! that  a  set  of  tires  would  run  2700  miles  in  average 
weather,  but  that  a  set  of  horses'  shoes  would  bear  only 
200  miles  of  travel.^: 

*  Penfolrt,  p.  22.  t  Gordon  on  Locomotion. 

t  The  impel  feet  surface  of  an  earth  road  makes  it  doubly  important 
to  take  every  precaution  to  lessen  the  friction  of  vehicles  upon  it.  The 
resistance  decreases  as  the  breadth  of  the  tire  increases,  on  compressible 
roada,  as  earth,  sand,  gravel,  &c. ;  while  on  paved  and  broken-stone  roads, 
the  resistance  is  nearly  independent  of  the  breadth  of  the  tire.*  Cylin- 
drical wheels  also  cause  less  friction  than  conical  ones.  The  larger  the 
wheels  the  less  friction  have  they,  and  the  greater  power  of  leverage  in 
overcoming  obstacles.  The  fore-wheels  should  be  as  large  as  the  hind  ones, 
were  it  not  for  convenience  of  turning.  The  axles  should  be  straight, 
and  not  bent  downward  at  the  end,  which  increases  the  friction,  though 
it  hoR  the  advantage  of  throwing  the  mud  away  from  the  carriage.  The 
If  ad  should  be  placed  on  the  hind  wheels  rather  than  on  the  fore  oaw 
*  Morin  p.  339. 


GRAVEL  ROADS.  193 


2.  GRAVEL  ROADS.* 

The  roundness  of  the  pebbles,  which  form  the  chief 
part  of  gravel,  whether  from  rivers  or  pits,  prevents  them 
from  perfectly  consolidating^  except  under  much  travel ; 
but  still  a  gravel  road,  properly  made,  is  far  superior  to 
one  of  common  earth.  Gravel  from  the  shores  of  rivers 
is  too  clean  for  this  object,  and  does  not  contain  enough 
earthy  matter  to  unite  and  bind  together  its  pebbles,  which 
are  too  perfectly  water-worn,  and  freed  from  asperities. 
On  the  other  hand,  gravel  dug  from  the  earth  contains  too 
much  earth,  which  must  be  sifted  from  it  before  use.  Two 
sieves  should  be  provided,  through  which  the  gravel  is  to 
be  thrown.  One  should  have  wires,  an  inch  and  a  half 
or  two  inches  apart,  so  that  all  pebbles  above  that  size 
may  be  rejected.  The  other  should  have  spaces  of  three 
quarters  of  an  inch,  and  the  material  which  passes  through 
it  should  be  thrown  away,  or  employed  for  foot-paths. 
The  expense  of  sifting  will  be  more  than  repaid  by  the 
superior  condition  of  the  road  formed  by  the  purified  ma- 
terial, and  the  diminution  of  labor  in  keeping  it  in  order. 

The  road-bed  should  be  well  shaped  and  drained.  If 
it  is  rock,  all  projecting  points  should  be  broken  off,  and 
a  layer  of  earth,  a  foot  thick,  should  be  interposed,  or  the 
gravel  will  wear  away  much  more  rapidly,  and  consoli- 
date much  more  slowly. 

Long  and  pliant  springs  greatly  lessen  the  shock  of  passing  over  obsta- 
cles, and  their  advantage  has  been  stated  to  be  equal  to  one  horse  in  four 
The  line  of  draught  should  ascend  at  an  angle  of  15  degrees,  so  that 
vvh^u  the  horse  leans  forward  in  pulling,  his  force  will  be  exerted  nearly 
Horizontally 
*  Parnell,  p.  170.  Penfold  p.  13.  Amer.  Railroad  Journal,  rol.  ii.  p.  4. 


194         IMPROVEMENT  OF  THE  SURFACE. 

A  coating  of  four  inches  of  gravel  should  be  spread 
over  the  road-bed,  and  vehicles  allowed  to  pass  over  it 
til  it  becomes  tolerably  firm,  and  is  nearly,  but  not  en- 
tirely, consolidated  ;  men  being  stationed  to  continually 
rake  in  the  ruts,  as  fast  as  they  appear.  A  second  coat- 
ing of  3  or  4  inches  should  then  be  added  and  treated  like 
the  first ;  and  finally  a  third  coating.  A  very  heavy  roller 
drawn  over  the  road  will  hasten  its  consolidation.  Wet 
weather  is  the  most  favorable  time  for  adding  new  ma- 
terials. 

A  very  erroneous  practice  is  that  of  putting  the  larger 
gravel  at  the  bottom,  and  the  smaller  at  the  surface  ;  for, 
from  the  effects  of  the  frost,  and  of  the  vibration  of  car- 
riages, the  larger  stones  will  rise  to  the  surface  and  the 
smaller  ones  descend,  like  the  materials  in  a  shaken  sieve, 
and  the  road  will  never  become  firm  arid  smooth. 

3.  BROKEN-STONE  ROADS. 

Broken-stone  roads  have  been  the  subjects  of  violent 
partisanship  on  many  disputed  points,  and  the  most  im- 
portant of  these  questions  relates  to  the  propriety  or  ne- 
cessity of  a  paved  foundation  beneath  the  coating  of  bro- 
ken stones.  McAdam  warmly  denies  the  advantages  of 
this,  while  Telford  supports  and  practises  it.  Broken- 
stone  roads  may  therefore  be  conveniently  divided  into 
McAdam  roads  and  Telford  roads. 

McADAM  ROADS. 

Mr.  McAdam,  who  first  brought  into  general  use  in 
.England  roads  of  broken  stone,  and  from  whom  they  de- 
rive their  popular  name,  is  said*  to  have  deduced  the 

*  MilliiiKton,  p.  234. 


McADAM    ROADS.  195 

leading  principles  of  his  improved  system  from  his  obser- 
vation of  the  passage  of  a  heavy  vehicle,  such  as  a  loaded 
stage-coach,  over  a  newly-formed  gravel  road.  The  wheels 
sink  in  to  a  considerable  depth,  and  plough  up  the  road, 
in  consequence  of  the  roundness  of  the  pebbles,  which 
renders  them  easily  displaced.  Hence  ensues  great  fric- 
tion against  the  wheels  ;  which,  moreover,  are  always  in 
hollows  with  little  hills  of  pebbles  in  front  of  them,  which 
they  must  roll  over  or  push  aside.  The  evil  continues, 
until  at  last,  after  long-repeated  passages  of  heavy  vehi- 
cles, the  pebbles  have  become  broken  into  angular  frag- 
ments, which  finally  form  a  compact  mass. 

But  since  this  is  so  desirable  a  consummation,  the  task 
of  breaking  the  stones  ought  not  to  be  imposed  on  the 
carriages,  but  should  be  performed  in  advance  by  manual 
labor,  by  which  it  will  be  executed  far  more  speedily, 
effectually,  and  completely. 

Hence  is  deduced  the  leading  principle  of  the  system, 
viz. :  that  the  stones  should  be  all  broken  by  hand  into 
angular  fragments  before  being  placed  on  the  road,  and 
that  no  rounded  stones  should  eve*  be  introduced. 

In  the  next  place,  whenever  a  carriage-wheel,  or  horse's 
hoof,  falls  eccentrically  on  a  large  stone,  it  is  loosened 
from  its  place,  and  disturbs  the  smaller  ones  for  a  consid- 
erable distance  around  it,  thus  preventing  their  consol- 
idation. Therefore  no  large  stones  should  be  ever  em- 
ployed. 

Small  angular  stones  are  the  cardinal  requisites.  When 
of  suitable  materials  of  proper  size,  and  applied  in  ac- 
cordance with  the  directions  which  will  be  presently  given, 
they  will  unite  and  consolidate  into  one  mass,  almost  as 
solid  as  the  original  stone,  with  a  smooth,  hard,  and  un- 
elastic  surface. 


f96  IMPROVEMENT    OF    THE    SURFACE. 

We  will  examine  successively  the  proper  quality  of 
stone  to  be  used ;  the  size  to  which  they  should  be  bro- 
ken ;  the  manner  of  breaking  them  •  the  thickness  of  the 
coating;  the  best  method  of  applying  the  stone  ;  of  rolling 
the  road  ;  of  keeping  it  in  order ;  and  of  repairing  it  when 
in  bad  condition. 

THE    QUALITY    OF    THE    STONE. 

The  materials  employed  for  a  broken-stone  road  (often 
called  the  "  Road  metal")  should  be  at  the  same  time 
hard  and  tough.  "  Hardness  is  that  disposition  of  a  solid 
which  renders  it  difficult  to  displace  its  parts  among  them- 
selves ;  thus,  steel  is  harder  than  iron,  and  diamond  al- 
most infinitely  harder  than  any  other  substance  in  nature. 
The  toughness  of  a  solid,  or  that  quality  by  which  it  will 
endure  heavy  blows  without  breaking,  is  again  distinct 
from  hardness,  though  often  confounded  with  it.  It  con- 
sists in  a  certain  yielding  of  parts  with  a  powerful  general 
cohesion,  and  is  compatible  with  various  degrees  of  elas- 
ticity."* 

Some  geological  knowledge  is  required  to  make  a 
proper  selection  of  the  materials.  The  most  useful  are 
those  which  are  the  most  difficult  to  break  up.  Such  are 
the  basaltic  and  trap  rocks,  particularly  those  in  which 
the  hornblende  predominates.  The  greenstones  are  very 
variable  in  quality.!  Flint  or  quartz  rocks,  and  all  pure 
silicious  materials,  are  improper  for  use,  since,  though 
hard,  they  are  brittle,  and  deficient  in  toughness.  Granite 
is  generally  bad,  being  composed  of  three  heterogeneous 


*  Sir  John  Herschel.    "  Discourse  on  the  study  of  Natural  Philosophy  " 
t  The  greenstone  of  Bergen  and  Newark  mountain  (near  New  York; 
is  good  ;  that  of  the  eastern  face  of  the  Palisades  above  Weehawkeu  fa 
too  liable  to  decomposition.     (Renwick,  Pract  Mechanics,  p.  145.) 


MCADAM    ROADS.  197 

materials,  quartz,  felspar,  and  mica,  the  first  of  which  is 
brittle,  the  second  liable  to  decomposition,  and  the  third 
laminated.  The  sienitic  granites,  however,  which  con- 
tain hornblende  in  the  place  of  felspar,  are  good,  and  bet- 
ter in  proportion  to  their  darkness  of  color.  Gneiss  is  still 
inferior  to  granite,  and  mica-slate  wholly  inadmissible. 
The  argillaceous  slates  make  a  smooth  road,  but  one  which 
decays  very  rapidly  when  wet.  The  sandstones  are  too 
soft.  The  limestones  of  the  carboniferous  and  transition 
formations  are  very  good  ;  but  other  limestones,  though 
they  will  make  a  smooth  road  very  quickly,  having  a  pe- 
culiar readiness  in  "binding,"  are  loo  weak  for  heavy 
loads,  and  wear  out  very  rapidly.  In  wet  weather  they 
are  also  liable  to  be  slippery.  It  is  generally  better  econ- 
omy to  bring  good  materials  from  a  distance  than  to  em- 
ploy inferior  ones  obtained  close  at  hand.  Excellent 
materials  may  be  found  throughout  the  primary  districts 
of  the  United  States.  In  the  tide-water  regions,  south  of 
New  York,  boulders,  or  rolled  pebbles,  must  be  employed. 

As  the  harder  stones  cost  much  more  to  break  than  the 
softer  ones,  the  lower  courses  of  the  road  may  be  formed 
of  the  latter,  and  the  former  reserved  for  covering  the 
surface,  which  has  to  resist  the  grinding  action  of  the 
wheels.*  * 

In  alluvial  countries,  where  stone  is  scanty  and  wood 
plenty,  an  artificial  stone  may  be  formed  by  making  the 
clay  into  balls,  and  burning  them  till  they  are  nearly  vit- 
rified. The  slag,  or  refuse,  of  iron  furnaces,  makes  an 
excellent  material.  The  stony  or  slaty  part  of  coal  may 


*  Tli's  is  the  practice  on  the  avenues  of  New  York ;  broken  gneiss  be- 
ing put  be'.ow,  and  covered  with  broken  boulders,  which  cost  three  times 
as  ranch  to  break 


198        IMPROVEMENT  OF  THE  SURFACE. 

be  used  near  collieries.     Cubes  of  iron  have  been  im- 
bedded among  the  stones  with  some  advantages.* 


SIZE    OF    THE    STONE. 

The  stone  should  be  broken  into  pieces,  which  are  ag 
nearly  cubical  as  possible,  (rejecting  splinters  and  slices) 
and  the  largest  of  which,  in  its  longest  dimensions,  can 
pass  through  a  ring  two  and  a  half  inches  in  diameter. 
In  reducing  them  to  this  size,  there  will  of  course  Fig.  108 
be  many  smaller  stones  in  the  mass.  These  are 
the  proper  dimensions,  according  to  Telford  and 
Parnell.]  Edgeworth  prefers  1^  inches.  Pen- 
fold^,  names  two  inches  for  brittle  materials.  If 
smaller  they  would  crush  too  easily ;  but  on  the 
other  hand,  the  less  the  size  of  the  fragments,  the  smaller 
are  the  interstices  exposed  to  be  filled  with  water  and  mud. 
The  tougher  the  stone,  the  smaller  may  it  be  broken 
The  less  its  size,  the  sooner  will  it  make  a  hard  road  ; 
and  for  roads  little  travelled,  and  over  which  only  light 
weights  pass,  the  stones  may  be  reduced  to  the  size  of 
one  inch. 

McAdam  argues  that  the  size  of  the  stone  used  on  a  road 
must  be  in  due  proportion  to  the  space  occupied  on  a  smooth 
level  surface,  by  a  wheel  of  ordinary  dimensions  ;  and,  as  it 
has  about  an  inch  of  contact  longitudinally,  therefore  every 
stone  in  a  road  exceeding  one  inch  in  diameter,  is  mischievous  ; 
for  the  one-sided  bearing  of  the  wheel  on  a  larger  stone  will 
tend  to  turn  it  over  and  to  loosen  the  neighboring  materials. 
But  this  argument  proves  too  much  ;  for  however  small  the 
stone  is,  there  must  be  a  moment,  just  as  the  wheel  is  leaving 
it,  when  the  pressure  is  one-sided,  and  therefore  tends  to  over- 
turn it.  Subsequently  McAdam  preferred  the  standard  of 

•  Paraell,  p.  245.  t  Ibid.  p.  133  !  Pages  14,  15 


McADAM    ROADS. 


199 


weight  to  that  of  size,  and  made  six  ounces  the  maximum, 
(corresponding  for  average  materials  to  cubes  of  1^  inches,  or 
2£  inches  in  their  longest  diagonal)  directing  his  overseers  to 
carry  a  pair  of  scales  and  a  6-oz.  weight,  with  which  to  try 
the  largest  stones  in  a  pile.  The  weight  standard  has  the  ad- 
vantage, that  the  stones  are  smaller  as  they  increase  in  speci- 
fic gravity,  to  which  the  hardness  is  generally  proportional. 
He  subsequently  says  that  he  had  "  not  allowed  any  stone 
above  three  ounces  in  weight  (equal  to  cubes  of  \\  inches,  or 
2  inches  in  their  longest  diagonal)  to  be  put  on  the  Bath  and 
Bristol  roads  for  the  last  three  years,  and  found  the  benefit  in 
the  smoothness  and  durability  of  the  work  as  well  as  economy 
of  repairs."*  On  examining  old  roads  he  found  that  the  aver- 
age size  of  the  stones  varied  from  seven  to  twenty-seven  ounces 
in  weight,  and  that  "  the  state  of  disrepair  and  the  amount 
of  expense  on  the  several  roads  was  in  a  pretty  exact  propor- 
tion to  the  size  of  the  material  used."f  The  French  engineers 
value  uniformity  of  size  much  less  than  Me  Adam,  and  call  it 
"  rather  an  evil  than  a  good."  They  therefore  use  equally  all 
sizes  from  l£  inches  to  dust.t 

Fig.  109. 


BREAKING    THE    STONE. 

The  weight  and  shape  of  the  hammer, 
and  the  manner  of  using  it,  are  of  much 
importance,  making  a  difference  of  at  least 
10  per  cent.  The  head  of  the  hammer 
should  be  six  inches  long,  and  weigh  about 
one  pound ;  and  the  handle  be  tough  and 
flexible,  and  3  feet  long,  if  used  standing, 
or  18  inches,  if  used  sitting,  which  is  better. 
The  laborer  sits  before  the  pile,  and  breaks 
the  stones  on  it,  or  on  a  large  concave  stone 
as  an  anvil,  on  which  the  stones  to  be  bro- 


»  Letter  of  1834,  in  Am.  Railroad  Journal,  Jan.  10,  1835. 
t  System  of  Roadmaking,  1825.  \  Gayffier,  p.  201. 


200 


IMPROVEMENT    OF    THE    SURFACE 


ken  are  placed,  resting  only  on  their  ends,  so  that,  being 
struck  sharply  in  their  middle,  they  break  into  angular 
fragments.  Children  with  smaller  hammers  can  do  the 
lighter  work,  so  that  a  whole  family  may  be  employed. 
The  workmen  should  not  be  paid  by  the  day,  but  at  an 
equitable  price  per  cubic  yard.  A  medium  laborer  car. 
break  in  a  day  from  1^  to  2  yards  of  gneiss  ;  but  only  ^ 
to  f  yard  of  hard  boulders,  or  "  cobble-stones." 


THICKNESS    OF    THE 


Twelve  inches  of  well  consolidated  materials  ou  a  good 
bottom,  will  be  sufficient  for  roads  of  Hie  greatest  travel, 
and  will  resist  all  usual  weights,  and  frosts.  In  the  cli- 
mate of  France,  ten  inches  is  considered  enough  for  the 
most  frequented  roads,  and  six  or  eight  inches  for  others. 
The  thickness  should  vary  with  the  soil,  the  nature  of  the 
materials,  and  the  character  of  the  travel  over  it  ;  it  should 
be  such  that  the  greatest  load  will  not  affect  more  than 
the  surface  of  the  shell  ;  and  it  is  for  this  purpose  chiefly 
that  thickness  is  required,  in  order  that  the  weight  whicb 
comes  on  a  small  part  only  of  the  road  may  be  spread 
over  a  large  portion  of  the  foundation.  The  severe  frosts 
of  our  northern  states  require  the  maximum  of  depth.* 

McAdam  advocates  less  thickness  than  the  other  Eng- 
lish constructors.  He  considers  from  7  to  10  inches  suffi- 
cient, calling  the  latter  depth  of  "  well  consolidated  mate- 
rials equal  to  carry  any  thing."  He  adds,  "  some  new 
roads  of  six  inches  in  depth  were  not  at  all  affected  by  a 
very  severe  winter  ;  and  another  road  having  been  allowed 

*  Stone  broken  into  fragments  of  from  1  to  6  inches  occupies  twice 
as  much  space  as  in  the  original  solid  state  ;  but  the  broken  stone  placed 
tipou  the  road  is  reduced  by  the  pressure  of  the  wheels  to  two  thirds 
of  its  former  bulk,  or  more  exactly  seven-tenths. 


McADAM    ROADS  201 

to  weai  down  to  only  three  inches,  this  was  f<5und  suffi- 
cient to  prevent  the  water  from  penetrating,  and  thus  to 
escape  any  injury  by  frost."  He  earnestly  advocates,  the 
principle  that  the  whole  science  of  artificial  road-making 
consists  in  making  a  solid  dry  path  on  the  natural  soil, 
and  then  keeping  it  dry  by  a  durable  water-proof  coating. 
'  The  broken  stone  is  only  to  preserve  the  under  road 
from  moisture,  and  not  at  all  to  support  the  vehicles,  the 
weight  of  which  must  be  really  borne  by  the  native  soil, 
which,  while  preserved  dry,  will  carry  any  weight,  and 
does  in  fact  carry  the  stone  road  itself  as  well  as  the  car- 
riages upon  it."  .  .  .  "The  stone  is  employed  to  "form  a 
secure,  smooth,  water-tight  flooring,  over  which  vehicles 
may  pass  with  safety  and  expedition  at  all  seasons  of  the 
year."  ..."  Its  thickness  should  be  regulated  only  by 
the  quantity  of  material  necessary  to  form  such  a  flooring, 
and  not  at  all  by  any  consideration  as  to  its  own  indepen- 
dent power  of  bearing  weight."  ..."  The  erroneous 
idea  that  the  evils  of  an  undrained  wet  clayey  soil  can  be 
remedied  by  a  large  quantity  of  materials,  has  caused  a 
large  part  of  the  cosily  and  unsuccessful  expenditures  in 
making  broken-stone  roads."* 

APPLICATION    OF    THE    MATERIALS. 

The  road-bed,  having  been  thoroughly  drained,  must 
be  properly  shaped  and  sloped  each  way  from  the  centre, 
so  as  to  discharge  what  water  may  penetrate  to  it,  and  not, 
as  is  often  practised,  be  made  level,  and  the  crowning 
given  by  a  greater  thickness  of  stone  in  the  middle. 
Upon  this  bed,  a  coating  of  three  inches  of  the  clean  bro- 
ken stones,  free  from  any  earthy  mixture,  is  to  be  spread 

*  McAdam — "  System  of  Road-making,"  passim. 


202         IMPROVEMENT  OF   HE  SURFACE. 

on  a  dry*  day.  The  travel  is  then  to  be  admitted  on  it, 
men  being  stationed  to  rake  in  the  ruts  as  soon  as  formed, 
or  a  heavy  roller  used,  till  it  becomes  almost  consolidated, 
but  not  completely  so,  (the  determination  of  this  time  being 
a  nice  and  important  practical  point)  and  a  second  coat  of 
three  inches  is  then  to  be  added  during  a  wet  time,  as 
moisture  greatly  facilitates  the  union  of  the  two.  A  third 
coat  is  added  as  was  the  second,  and  a  fourth  if  that  be 
required.  If  the  stone  be  very  hard,  and  the  wheeling 
very  difficult,  fine  clean  gravel,  free  from  earth,  may  be 
spread  over  the  surface;  but  it  is  better  for  the  future 
solidity  of  the  road  to  dispense  with  this,  if  possible. 

If  a  thick  coat  be  laid  on  at  once,  there  is  a  very  great 
destruction  of  the  material  before  it  becomes  consolidated, 
if  it  ever  dees  so.  The  stones  will  not  allow  one  another 
to  be  quiet,  but  are  continually  elbowing  each  other,  and 
driving  their  neighbors  to  the  right  and  to  the  left.  This 
constant  motion  rapidly  wears  off  the  angular  points,  and 
reduces  the  stones  to  a  spherical  shape,  which,  in  con- 
junction with  tjie  amount  of  mud  and  powder  produced, 
destroys  the  possibility  of  any  firm  aggregation,  and  the 
road  never  attains  its  proper  condition  of  hardness.* 

The  broken  stones  need  not  be  spread  over  a  greater 
width  than  from  12  to  16  feet,  (except  near  large  cities) 
and  "  wings"  of  earth  may  be  left  on  each  side.  For  a 
road  little  used  a  single  track  of  8  feet  of  the  "  metal"  will 
suffice.! 

The  perfect  cleanliness  of  the  stones  is  strongly  insisted  on 
by  McAdam.  He  directs  the  broken  stones  to  be  very  carefully 
kept  perfectly  free  from  any  mixture  of  earth,  or  any  matter 
which  will  imbibe  water,  or  be  affected  by  frost ;  since  roads 

»  Penfold,  p.  15  t  See  page  47. 


McAtAM    ROADS.  203 

made  with  such  a  mixture  become  loose  in  wet  weather,  and  al- 
low the  wheels  of  carriages  to  displace  the  materials,  and  to  cut 
through  to  the  original  soil,  thus  making  the  roads  rough  and 
rutty,  the  admission  of  water  being  the  great  evil.  He  adds 
that  nothing  must  be  laid  on  the  clean  stone  under  the  pretence 
of  "  binding  ;"  for  clean  broken  stone  will  combine  by  its  own 
angles  into  a  smooth  solid  surface,  which  cannot  be  affected 
by  vicissitudes  of  weather,  nor  displaced  by  the  action  of 
wheels. 

The  French  engineers  consider  this  cleanliness  as  unneces- 
sary, since  the  travelling  on  the  road  very  soon  pulverizes  the 
materials,  and  fills  the  interstices  with  dust  and  mud  ;  though 
it  might  be  replied  that  this  took  place  only  on  the  surface. 
Some  of  them,  observing  the  large  amount  of  vacant  space  in 
a  mass  of  broken  stone,*  have  even  proposed  to  combine  with 
it  in  advance  a  certain  proportion  of  calcareous  stone,f  or  even 
clay  and  sand.J  just  sufficient  to  fill  up  the  existing  vacancies. 
This  would  doubtless  make  a  road  tolerably  fit  for  use  much 
sooner  than  the  regular  plan,  but  its  permeability  to  water 
would  entail  on  it  all  the  evils  mentioned  in  the  preceding  par- 
agraph. 

*  A  cubic  metre  of  broken  stones,  placed  in  a  water-tight  box, 
which  they  just  fill,  can  receive  in  the  empty  spaces  between  the 
fragments  a  volume  of  water  =  -j-4680,  or  nearly  one-half  of  the  whole 
the  actual  solidity  of  the  stones  being  therefore  only  j^-  This  doee 
not  vary  for  stones  from  1  to  8  inches  in  size.  After  prolonged  travel 
it  increases  to  yB!ff,  leaving  a  void  of  only  T2^.  For  rolled  pebbles 
and  sand  the  actual  solidity  may  be  as  much  as  T6/ff.  For  perfect 
spheres,  calculation  shows  that  the  solidity  of  a  mass  of  them  in- 
creases as  their  diameter  decreases.  Thus,  if  a  cubic  metre  be  filled 
with  spheres  4  inches  in  diameter,  their  solid  volume  will  be  ~^  ;  if 
they  are  1  inch  in  diameter  their  volume  is  j^e  ;  and  if  only  -Jj  inch 
it  K  lYo-  Pebbles  by  theory,  as  well  as  by  the  experiment  above 

cited,  would  be  intermediate  between  broken  stones  and  spheres 

(Gayffier,  pp.  204  to  214.) 

1  M.  Polouceau.  M  Girard  de  Caudemberg. 


204  IMPROVEMENT    OF    THE    SURFACE. 


The  use  of  a  very  heavy  roller  will  much  facilitate  the 
consolidation  of  the  road.  A  plan  highly  recommended 
is  to  have  a  roller  made  of  a  hollow  cylinder,  of  cast  iron, 
or  covered  with  iron  bands,  seven  feet  in  diameter,  and 
five  feet  long.  A  strong  axle  passes  through  its  length. 
Its  ends  are  closed,  and  two  interior  partitions,  perpendic- 
ular to  the  axis,  divide  it  into  three  equal  chambers.  A 
longitudinal  band  of  the  surface,  a  foot  wide,  can  be  de 
tached,  so  as  to  give  access  to  the  interior  spaces,  which 
are  filled  with  gravel,  one  or  all  of  them,  according  to  the 
weight  desired.  The  empty  cylinder  weighs  7000  Ibs. ; 
each  compartment  filled  with  gravel  adds  4,000  Ibs.  to 
the  weight ;  so  that  the  entire  weight  may  be  made  suc- 
cessively 7,000  Ibs.,  11,000  Ibs.,  15,000  Ibs.,  and  19,000 
Ibs.  To  compress  a  new  road,  ten  or  twelve  strong  horses 
should  be  attached,  on  a  wet  day  in  summer,  to  the  empty 
roller,  and  draw  it  several  times  over  every  part  of  the 
road,  till  the  materials  have  been  so  far  compressed  as  not 
to  form  a  ridge  in  front  of  the  roller.  Then  the  middle 
division  is  to  be  filled  with  gravel,  (moistened,  to  give  it 
solidity)  and  the  rolling  resumed  till  the  draught  is  so  much 
lessened  that  the  end  divisions  can  be  filled,  the  middle 
one  being  emptied  at  first  if  necessary.  There  should  be 
an  excess  of  power  in  the  horses,  so  that  they  may  do 
•ess  injury  by  the  viole'nt  pressures  of  their  feet.  Every 
part  of  the  road  should  be  passed  over  from  40  to  100 
times.  To  increase  the  stability  of  the  compression  ob 
tained,  an  inch  of  gravel  should  be  spread  over  the  surface 
and  passed  over  by  the  roller  a  few  limes.  If  the  weather 

*  Gayffier,  p.  212 


MCADAM    ROADS.  205 

he  dry.  the  surface  should  be  watered.  The  season  should 
be  summer,  that  the  road-bed  may  be  dry,  and  the  day  be 
wet,  to  ensure  a  moist  surface,  which  facilitates  the  bind- 
ing of  the  materials. 

When  the  rolling  has  finished  the  compression,  the 
road  is  still  very  different  from  one  which  has  borne  the 
traffic  of  many  years  ;  for  although  the  materials  are 
strongly  pressed  against  one  another,  and  have  taken 
a  stable  position,  they  have  not  acquired  the  adhesion 
which  takes  place  after  a  series  of  years.  The  new  road, 
therefore,  needs  for  some  time  most  careful  attention. 
The  travel  must  finish  it  by  being  forced  to  pass  over 
every  part  of  it  uniformly,  heaps  of  pebbles  being  placed 
very  irregularly,  so  as  to  direct  the  vehicles  successively 
on  all  the  points  of  the  road.  Every  rut,  and  the  slightest 
hollows  and  elevations,  must  be  promptly  removed  by  a 
liberal  supply  of  laborers,  whose  work  will,  however 
have  been  greatly  lessened  by  the  previous  rolling.  The\ 
must  rake  over  every  inequality  of  surface  the  momen. 
that  it  is  formed. 

KEEPING    UP    A    ROAD. 

This  is  a  very  different  thing  from  "  repairing  a  road," 
though  the  two  are  often  confounded.  A  due  attention  to 
the  former  will  greatly  lessen  the  necessity  for  the  latter. 
The  former  keeps  the  road  always  in  good  condition  ;  the 
latter  makes  it  so  only  occasionally,  after  intervals  of  va 
rious  length,  during  which  it  is  continually  deteriorating 
in  a  geometrical  ratio,  so  that  the  better  the  state  in  which 
the  road  is  kept,  the  less  are  the  injuries  to  it,  and  there- 
fore, the  less  the  expense  of  keeping  it  in  this  excellent 
condition. 

"  Keeping  up  the  road"  requires  the  daily  attention  oi 


206  IMPROVEMENT    OF    THE    SURFACE. 

a  permanent  corps  of  laborers.  Supposing  the  road  to  be 
already  in  good  condition  ;  that  is,  in  proper  shape,  and 
free  from  holes,  ruts,  mud,  and  dust ;  to  keep  it  so,  re- 
quires two  fundamental  operations : 

1 .  The  continual  removal  of  the  daily  wear  of  the  ma 
terials,  whether  in  the  shape  of  mud  or  of  dust ; 

2.  The    employment    of    materials   to   replace    those 
removed. 

The  first  operation  requires  hoes  and  brooms.  The 
hoes  should  be  three  feet  long,  and  of  wood,  as  iron  ones 
would  be  more  likely  to  loosen  the  stones.  The  lighter 
dust  and  more  liquid  mud  must  be  swept  off  by  birch 
brooms.  The  detritus  between  the  little  projections  oi 
the  stones  should  not  be  removed  by  too  thorough  sweep- 
ing, as  it  protects  them  from  immediate  crushing,  and 
preserves  their  stability.  The  broom  is  also  necessary  to 
remove  every  trace  of  wheels,  the  moment  they  have 
passed,  so  as  to  oppose  that  habit  or  instinct  of  horses 
which  leads  them  to  follow  in  the  track  of  the  preceding 
vehicle,  and  which  would  soon  convert  unremoved  tracks 
into  ruts.  The  broom  and  hoe  have  then  a  double  end 
to  be  accomplished  by  the  same  operation,  viz.,  effacing 
tracks  and  removingdetritus.  Very  effective  machines  have 
also  been  constructed  for  accomplishing  these  purposes.* 

The  second  operation  of  applying  new  materials  de- 
mands several  precautions.  To  prevent  a  weak  place 
from  being  neglected  because  the  materials  are  not  at 
hand,  they  should  be  kept  in  depots,  never  more  than  a 
quarter  of  a  mile  apart,  and  carried  thence  in  barrows. 
They  should  be  applied  after  a  rain,  as  then  they  will 
more  easily  unite,  and  no  coat,  thicker  than  one  stone, 

»  Roads  and  Railroads,  p.  91 


MrADAM    ROADS.  207 

should  ever  be  applied  at  any  one  time.  A  cubic  yard  to 
a  superficial  rod  will  be  quite  enough  at  once.  They  will 
then  soon  become  incorporated  without  having  their  angles 
worn  out  by  motion,  and  will  be  of  as  much  service  as 
double  the  thickness  applied  at  once.  To  avoid  retarding 
the  travel  and  increasing  the  draught  too  much,  a  new 
coat  should  not  be  put  on  any  continuous  space  larger 
than  six  or  seven  square  yards.  If  several- depressions 
are  found  very  near  each  other,  cover  the  worst,  and  at- 
tend to  the  next  after  the  first  has  become  solid.  The 
ruts  which  are  formed  should  not  be  filled  with  loose 
stone,  for  this  would  make  longitudinal  ridges  of  harder 
material,  but  "  the  laborer  should  work  the  rake  back- 
wards and  forwards  on  each  side  of  the  rut  and  across  it ; 
and  if  he  do  it  with  his  eyes  shut,  he  will  do  more  good, 
than  by  taking  pains  to  gather  all  the  stones  he  can  find  to 
place  in  it."* 

The  number  of  men  required  by  this  system  of  con- 
stant watchfulness  may  at  first  seem  an  objection  to  it, 
but  the  expense  will  be  amply  repaid  by  the  advantages 
obtained.  Each  laborer  should  have  a  certain  length  of 
the  road  assigned  to  his  especial  care,  and  the  most  intel- 
ligent and  trustworthy  among  them  should  be  made 
inspectors  over  the  others  for  a  certain  distance.  At 
times  unfavorable  for  work  'on  the  road,  they  should  be 
employed  in  breaking  stone.  The  labor  of  one  man  wil! 
keep  in  repair  three  miles  of  well-made  and  well-drained 
roa'd,  for  the  first  two  years  after  its  formation,  and  four 
miles  for  the  next  two  years,  by  constantly  spreading 
loose  stones  in  the  hollows,  raking  them  from  the  middle 
to  the  sides,  opening  the  ditches,  &c.  In  the  fifth  year 


»  Tenfold,  p.  20 
14 


208  IMPROVEMENT    OF    THE    SURFACE 

some  repairs,  "  with  lifting,"  may  be  necessary,  as  ex- 
plained under  the  next  head.* 

It  will  be  seen  by  Morin's  table,  on  page  63,  that  the 
friction  or  resistance  to  draught  on  a  road  with  deep  ruts 
and  thick  mud,  is  four  times  as  great  as  on  one  in  good 
order.  This  shows  the  importance  of  very  perfectly 
"  keeping  up"  the  road.  An  incidental  advantage  is  that 
the  prompt  removal  of  the  mud  after  every  shower  will 
prevent  the  annoyance  of  dust,  so  general  an  objection  to 
McAdam  roads,  but  not  at  all  their  necessary  concern 
itant. 

Where  the  materials  of  the  road  are  very  brittle  stone, 
they  wear  away  very  rapidly  in  dry  weather,  and  their 
consumption  may  be  much  lessened  by  watering  the  road 
judiciously  ;  not  so  little  as  to  form  a  crust  which  adheres 
to  the  wheel,  nor  so  much  as  to  make  the  draught  heavy. 
A  moderate  use  of  the  watering  cart  preserves  the  mate- 
rials from  pulverization,  and  keeps  them  settled  in  their 
places,  at  the  same  time  that  the  comfort  of  the  traveller 
is  greatly  enhanced.  This  is  particularly  necessary  on 
roads  in  this  country  during  our  hot  and  dry  summers  ; 
for  after  a  long  drought  the  crust  of  the  road  sometimes 
becomes  so  dried  out  that  it  ceases  to  "  bind,"  and  per- 
mits loose  stones  to  be  detached  from  it,  to  the  great 
injury  of  the  surface.  An  excess  of  moisture  must,  how- 
ever, be  avoided,  since  it  increases  the  grinding  power  of 
ihe  pulverized  stones,  as  marble  is  sawn  and  jewels  are 
cut  with  their  own  powder  combined  with  water. 

The  question  may  arise,  whether  the  materials  thus 
gradually  added  to  the  road,  for  alimentation  rather  than 
reparation,  are  sufficient  to  make  up  for  its  annual  loss, 

•  See  Am.  Railroad  Journal,  March  13,  1847. 


McADAM    ROADS.  20P 

and  diminution  of  depth,  which  is  too  small  for  direct 
measurement.  Experiments  upon  this  point  indicate  that 
the  amount  of  materials  annually  consumed,  and  therefore 
to  be  replaced,  is  one  cubic  yard  per  mile*  for  each  "  col- 
lar," or  beast  of  burden  passing  over  it.  Others  consider 
it  only  two-thirds  of  a  cubic  yard.f 

REPAIRING    A    ROAD. 

A  road  properly  kept  up  by  daily  attention,  needs  no 
repairs ;  but  if  it  be  put  in  order  only  at  intervals,  the 
injuries  to  it,  which  have  been  increasing  in  geometrical 
progression,  will  render  tery  serious  repairs  necessary. 
It  will  be  found  cut  into  ruts,  deep  holes,  and  irregular 
projections  ;  and  often  lower  in  the  middle  than  at  the 
sides.  It  must  be  put  into  shape,  and  restored  to  its 
proper  cross-section,  by  cutting  down  the  sides,  and  filling 
up  the  middle  part.  Only  a  single  thin  coat  of  stone 
should  be  applied  at  a  time, — not  more  than  a  cubic  yard 
to  a  rod  superficial.  The  surface  of  the  old  road  may  be 
lightly  picked  up,  or  "  lifted,"  (with  strong  short  picks) 
merely  burying  the  point  of  the  pick  one  or  two  inches 
deep,  so  that  the  new  materials  may  be  more  readily 
united  to  the  old  ones.  This  is  especially  necessary  on 
declivities,  to  prevent  the  stones  rolling  down  the  slope. 

When  the  road  to  be  repaired  is  one  which  had  been 
originally  formed  of  large  stones,  and  of  superfluous 
thickness,  no  new  materials  should  be  brought  upon  it, 
but  the  old  stones  should  be  loosened  with  picks,  gathered 
by  strong  rakes  to  the  side  of  the  road,  and  there  broken 
to  the  proper  size.  The  surface  of  the  road  having  been 
put  in  proper  shape,  the  broken  stones  are  to  be  returned 

*  DUPUIS,  Annales  des  Fonts  et  Chausees,  1842       t  Gayffier,  p.  232. 


2'0        IMPROVEMENT  OF  THE  SURFACE. 

to  it,  being  scattered  uniformly  and  thinly  over  the  sur- 
face. Only  a  small  space  of  road  should  be  thus  broken 
up  at  once,  say  six  or  eight  feet  in  length,  but  the  whole 
width.  The  old  plan  of  repairing  would  be  to  fill  up  the 
holes  with  an  additional  supply  of  the  same  large  mate 
rials  ;  but  the  method  here  recommended  makes  more 
work  for  men  and  less  for  horses,  and  produces  a  great 
saving  in  expense. 

The  best  season  for  repairing  broken-stone  roads  is  in 
the  spring  or  early  summer,  when  the  weather  is  neither 
very  wet  nor  very  dry,  for  either  of  these  extremes  pre 
vents  the  materials  from  consolidating,  and  therefore  pro- 
duces either  a  heavy  or  a  dusty  road.  If  made  at  this 
season,  the  roads  are  left  in  a  good  state  for  the  summer, 
and  become  consolidated  and  hard,  so  as  to  be  in  a  condi 
tion  to  resist  the  work  of  the  ensuing  winter.* 

TELFORD  ROADS. 

This  name  may  be  given  to  the  roads  of  broken  stone 
which  rest  on  a  peculiar  pavement,  as  constructed  by  Tel- 
ford,  on  the  Holyhead  road  and  elsewhere,  and  of  which 
he  has  given  the  following  specification  for  a  width  of 
thirty  feet.  Fig.  110  is  a  section  of  the  carriage-way  of 
such  a  road. 

Fig.  110. 


"  Upon  the  level  bedt  prepared  for  the  road  materials 

«  James  Walker. 

t  A  bed  with  the  same  cross-section  as  the  final  road,  would  certaislj 
DO  preferable,  to  ensure  drainage.  The  {lavement  would  then  require  to  b« 
of  the  same  depth  at  centre  and  sides. 


TELFORD    ROADS.  211 

a  bottom  course  or  layer  of  stones  is  to  be  set  by  hand  in 
the  form  of  a  close,  firm  pavement.  The  stones  set  in 
the  middle  of  the  road  are  to  be  seven  inches  in  depth ; 
at  nine  feet  from  the  centre,  five  inches  ;  at  twelve  from 
the  centre,  four  inches  ;  and  at  fifteen  feet,  three  inches.* 
They  are  to  be  set  on  their  broadest  edges  and  lengthwise 
across  the  road,  and  the  breadth  of  the  upper  edge  is  not 
to  exceed  four  inches  in  any  case.  All  the  irregularities 
of  the  upper  part  of  the  said  pavement  are  to  be  broken 
off  by  the  hammer,  and  all  the  interstices  to  be  filled  with 
stone  chips,  firmly  wedged  or  packed  by  hand  with  a  light 
hammer,  so  that  when  the  whole  pavement  is  finished, 
there  shall  be  a  convexity  of  four  inches  in  the  breadth  ot 
fifteen  feet  from  the  centre. 

"  The  middle  eighteen  feet  of  pavement  is  to  be  coated 
with  hard  stones  to  the  depth  of  six  inches.  Four  of  these 
six  inches  are  to  be  first  put  on  and  worked  in  by  car- 
riages and  horses  ;  care  being  taken  to  rake  in  the  ruts 
until  the  surface  becomes  firm  and  consolidated,  after 
which  the  remaining  two  inches  are  to  be  put  on.  The 
whole  of  this  stone  is  to  be  broken  into  pieces  as  nearly 
cubical  as  possible,  so  that  the  largest  piece,  in  its  longest 
dimensions,  may  pass  through  a  ring  of  two  inches  and  a 
half  inside  diameter. 

"  The  paved  spaces,  on  each  side  of  the  eighteen  middle 
feet,  are  to  be  coated  with  broken  stones,  or  well  cleansed, 
strong  gravel,  up  to  the  footpath  or  other  boundary  of  the 
road,  so  as  to  make  the  whole  convexity  of  the  road  six 
inches  from  the  centre  to  the  sides  of  it.  The  whole  of 
the  materials  are  to  be  covered  with  a  binding  of  an  inch 


*  The  curved  section  thus  obtained,  has  been  shown,.on  page  50,  to  be 
inferior  to  plane  slopes  on  each  side  of  the  centre 


212        IMPROVEMENT  OF  THE  SURFACE. 

and  a  half  in  depth,  of  good   gravel,  free  from  clay  of 
earth."* 

The  propriety  of  this  foundation,  ("Bottoming"  ot 
"  Pitching")  has  been  the  subject  of  earnest  controversy 
between  the  partisans  of  McAdam  and  those  of  Teiford. 
The  following  are  the  defects  imputed  to  a  road  of  broken 
stones,  laid  on  earth,  (especially  clay)  without  any  foun- 
dation. 

The  weight  of  vehicles  forces  the  lower  stones  into  the 
earth,  which  rises  up  into  the  interstices  and  forms  a  mix- 
ture of  earth  and  stones  which  will  always  be  loose  and 
open,  and  never  consolidate  into  a  compact  mass.  In  win- 
ter the  water,  which  will  penetrate,  is  frozen  and  breaks 
up  the  road.  After  a  thaw  and  in  wet  weather,  the  road 
is  a  quagmire,  the  wheels  cut  deeply  into  it,  and  some 
times  through  the  entire  thickness,  so  that  it  resembles  a 
ploughed  field.  At  the  best,  after  a  rain  the  semi-fluid 
soil  will  rise  up  to  the  surface  and  form  a  coat  of  mud  ; 
and  after  a  drought  the  looseness  of  the  stones  will  make 
them  rub  off  their  angles  and  soon  wear  out.  Nor  will 
any  thickness  of  broken  stones  thoroughly  destroy  the  elas- 
ticity of  the  soil,  the  evils  of  which  were  shown  on  page  58 

McAdam  maintains  that  thorough  draining  will  prevent 
all  these  evils,  but  Teiford  thinks  that  they  can  be  re- 
moved only  by  the  "  bottoming,"  for  which  he  claims  the 
following  advantages. 

Roads,  being  in  fact  artificial  structures,  which  have  to 
sustain  great  weights  and  violent  percussion,  the  first  object 
must  be  to  obtain  a  permanently  firm  and  stable  foundation. 

This  is  effected  by  the  plan  of  "  bottoming  ;"  for  by  it 
the  pressure  of  the  wheels  is  distributed  over  a  large 


*  Parnell,  pp.  133-4. 


TELFORD    ROADS  21Jf 

space.  Suppose  that  the  wheel  touches  and  presses  on  a 
surface  of  2  square  inches.  This  pressure  is  carried  to 
the  foundation  stones,  which  rest  at  their  bottom  on  a  broad 
surface,  averaging  10  by  5  inches,  or  50  square  inches, 
so  that  each  square  inch  of  the  soil  receives  only  one- 
twenty-fifth  part  of  the  surface  pressure,  and  there  is 
therefore  no  danger  of  the  pavement  stones  being  pressed 
into  it,  nor  of  the  soil  being  forced  to  ooze  up  between 
them.  On  a  new  embankment  of  soft  earth  it  is  best  to 
lay  brush  or  furze,  and  place  the  pavement  upon  this. 

The  advantages  of  this  system  are  most  striking  when 
the  natural  soil  is  retentive  of  moisture,  as  when  it  is  clay. 
The  pavement  then  acts  as  an  under-drain  to  carry  off  the 
water  which  may  find  its  way  through  the  broken-stone 
surface.  Even  on  a  rock  this  pavement  may  be  laid  with 
advantage,  to  form  a  clear  floor. 

When  the  stones  are  properly  set,  and  wedged  with  the 
stone  chippings,  they  will  never  rise  to  the  surface.*  To 
avoid  disturbing  them,  the  carts  which  bring  the  broken 
stone  must  not  be  allowed  to  pass  over  the  foundation. 

From  the  moment  that  a  road  thus  made  begins  to  be 
used,  it  becomes  daily  harder  and  smoother.  The  strength 
of  the  resulting  surface  admits  of  carriages  being  drawn 
over  it  with  the  least  possible  distress  to  horses.  The 
broken  stones  being  on  an  immoveable  dry  bed,  do  not 

*  Large  stones,  placed  under  a  road  and  not  thus  wedged  down,  will 
invariably  work  up  to  the  surface.  Thus,  over  Breslington  Common, 
England,  the  whole  of  the  original  soil  had  been  covered  at  great  ex- 
pense with  large  flag-stones,  and  the  road-covering  laid  upon  them.  Their 
motion  kept  the  surface  in  a  loose,  open  state,  till,  on  the  road  being  dug 
open,  they  were  found  almost  entirely  turned  upon  their  edges,  having 
been  acting  with  the  force  of  levers  upon  the  road,  which  they  had  made 
to  crack  and  sink,  without  the  rause  at  such  a  depth  being  suspected. — 
McAdani. 


214         IMPROVEMENT  OF  THE  SURFACE. 

mix  with  the  soil,  and  become  perfectly  united  together 
into  one  solid  mass. 

The  parts  of  the  Holyhead  road  formed  with  such  a 
foundation,  were  unaffected  by  a  series  of  unusually  se- 
vere frosts,  followed  by  thaws  and  heavy  rains,  while  the 
parts  of  it  differently  made,  and  other  roads  in  the  neigh 
borhood,  were  broken  up,  and  "  became  as  bad  as  a 
bog."* 

A  road  thus  constructed  will  in  most  cases  cost  less 
than  one  entirely  of  broken  stone  ;  for  the  course  of  foun- 
dation-stones may  be  of  any  cheap  and  inferior  stone,  as 
sand-stone,  &c.,  which  will  bear  weight,  and  not  be  de- 
composed by  the  atmosphere,  but  which  would  not  be 
sufficiently  hard  and  tough  for  the  broken-stone  covering. 
The  cost  of  hammering  and  setting  this  pavement  will  be 
less  than  that  of  breaking  up  an  equal  mass,  and  the  total 
amount  of  stone  employed  will  be  no  more  than  would 
have  been  required  for  a  road  entirely  of  broken  stone. 

But  even  if  such  a  road  cost  more  at  first,  it  would  be 
cheaper  in  the  end  ;  for,  beside  the  saving  of  draught, 
stones  laid  on  such  a  pavement  last  much  longer  than 
those  laid  on  earth,  two  courses  of  the  former  outlasting 
three  of  the  latter.  The  expense  of  scraping  is  lessened 
in  the  same  or  even  a  greater  proportion. 

On  the  other  hand,  it  is  objected  that,  between  the  wheel 
above  and  the  foundation-stone  beneath,  the  broken  stone 
will  be  in  a  situation  like  that  of  the  grain  between  two 
millstones,  and  must  therefore  be  more  rapidly  ground  to 
powder  than  if  on  a  soft  bottom.!  But  this  will  be  pre- 
vented by  using  harder  stone  for  the  surface  than  for  the 
foundation. 

*  Telford      First  Report  on  Holyhead  roads.  t  Peufold,  p  8 


1-ELFORD    ROADS.  215 

McAdam  also  maintains  that  the  materials  last  longer 
on  a  soft  and  elastic  bottom  than  on  a  hard  one ;  and  in- 
stances a  road  in  Somersetshire,  where  a  part  of  it  is 
"  over  a  morass  so  extremely  soft  that  when  you  ride  in 
a  carriage  along  the  road,  you  see  the  water  tremble  in 
the  ditches  on  each  side,"  and  is  succeeded  by  a  bottom 
of  limestone  rock,  continuing  for  five  or  six  miles.  An 
exact  account  of  the  expenditure  on  each  having  been  kept, 
it  was  found  that  the  cost  of  keeping  up  the  soft  was  to 
that  of  the  hard  only  as  five  to  seven  ;  i.  e.  five  tons  of 
stone  on  the  former  would  last  as  long  as  seven  on  the 
latter.  But  this  seems  an  exceptional  case,  being  con- 
trary to  all  other  experience.  Sir  John  Macneill  testifies 
very  strongly  that  the  annual  saving  of  a  paved  bottom 
will  be  one-third  of  the  expense  in  any  case,  and  that  if 
the  diminished  amount  of  horse  labor  were  considered,  it 
would  be  very  considerably  more  than  that.* 

An  artificial  substitute  for  a  pavement  foundation,  consist- 
ing of  a  concrete,  or  composition  of  Roman  cement  and  gravel, 
lias  been  employed  with  great  success  on  a  wet  and  elastic 
soil,  where  every  thing  else  had  failed,  and  where  stones  for 
bottoming  would  have  been  very  expensive.  The  locality  was 
the  Highgate  Archway  Road  near  London,  in  a  deep  cutting 
between  two  higb  banks  of  clay,  where  the  soil  was  surcharged 
with  water.  Many  attempts  at  draining  had  been  made,  and 
a  great  thickness  of  broken  stone  had  been  used,  and  subse- 
q^iently  relaid  on  furze  and  pieces  of  waste  tin.  But  the  stone 
mixed  with  the  wet  clay,  and  rapidly  wore  away,  becoming 
round  and  smooth,  without  ever  consolidating,  and  the  road 
was  almost  impassable.  The  Parliamentary  Commissioners 
finally  took  charge  of  it,  and  Sir  John  Macneill  succeeded  in 
making  a  perfect  road.  Four  longitudinal  drains  were  made 
the  whole  length  of  the  road,  cross  drains  at  every  90  feet,  and 

•  Parnell,  p.  163. 


216  IMPROVEMENT    OF    THE    SURFACE. 

intermediate  small  drains  at  every  30  feet  under  the  cement.* 
On  the  prepared  centre,  of  eighteen  feet  in  width,  after  it  had 
been  properly  levelled,  was  put  a  layer,  six  inches  thick,  of 
the  concrete,  formed  of  one  part  of  Roman  cement,  one  of 
sand,  and  eight  of  stones.  The  sand  and  cement  were  mixed 
dry  in  a  large  shallow  trough  ;  the  gravel  was  added  ;  as  little 
^vater  as  possible  was  used  ;  and  the  whole  mixture  was  then 
cast  upon  the  ground.  Before  it  had  set,  a  triangular  piece  of 
wood  was  indented  into  the  surface,  so  as  to  leave,  at  every 
four  inches,  a  triangular  groove  for  the  broken  stones  to  lie 
in  and  fasten  into.  These  grooves  fell  three  inches  from  the 
centre  to  the  sides  of  the  road,  in  order  to  carry  off  any  water 
which  might  percolate  through  the  broken  stones  above  it.  Six 
inches  of  these  were  laid  upon  it  when  it  had  sufficiently  hard- 
ened, (which  was  in  about  fifteen  minutes)  and  the  sides  or 
wings  were  filled  up  with  flint  gravel.  The  concrete  cost  at 
that  place  50  cents  per  square  yard  six  inches  thick.  The 
object  was  to  attain  a  dry  and  solid  foundation  for  the  broken 
stone.  The  result  was  an  excellent  road,  undisturbed  by  se- 
vere frosts,  and  on  which  one  horse  could  draw  as  much  as 
three  in  its  original  state. 


4.  PAVED   ROADS.T 

A  good  pavement  should  offer  little  resistance  to  wheels, 
but  give  a  firm  foothold  to  horses  ;  it  should  be  so  durable 
as  to  seldom  require  taking  up  ;  it  should  be  as  free  as 
possible  from  noise  and  dust  ;  and  when  it  is  laid  in  the 
streets  of  a  city,  it  should  be  susceptible  of  easy  removal 
and  replacement  to  give  access  to  gas  and  water  pipes. 

A  common  but  very  inferior  pavement,  which  disgraces 
the  streets  of  nearly  all  our  cities,  is  constructed  of  rounded 

»  See  Paruell,  pp.  157  and  160,  and  plates  to  Simms  on  Roads. 

1  Gayffier,  pp.  193-8  ;  Marlette,  pp.  104-8  ;  Jullien,  pp.  316-18  ;  Parncll, 
pp.  110-123,  348-359  ;  Mahan,  pp.  292-5  ;  Journal  of  Franklin  Insti- 
tute, Sept  Oct.  1843. 


STONE    PAVEMENTS.  217 

water-worn  pebbles,  or  "  cobble-stones."  The  best  are  of 
an  egg-like  shape,  from  5  to  10  inches  deep,  and  of  a 
diameter  equal  to  half  their  depth.  They  are  set  with 
their  greatest  length  upright,  and  their  broadest  end  upper- 
most. Under  them  is  a  bed  of  sand  or  gravel  a  foot  or 
two  deep.  They  are  rammed  over  three  limes,  and  a  layer 
of  fine  gravel  spread  over  them  to  fill  their  interstices.* 

The  glaring  faults  of  this  pavement  are  that  the  stones, 
being  supported  only  by  the  friction  of  the  very  narrow 
space  at  which  they  are  in  contact,  are  easily  pressed 
down  by  heavy  loads  into  the  loose  bottom,  thus  forming 
holes  and  depressions  ;  and  at  best  offer  great  resistance 
to  draught,  cause  great  noise,  cannot  be  easily  cleaned, 
and  need  very  frequent  repairs  and  renewals.! 

The  pavement  which  combines  most  perfectly  all  desira 
ble  requisites,  is  formed  of  squared  blocks  of  stone,  rest- 
ing on  a  stable  foundation,  and  laid  diagonally. 

We  will  examine  successively  the  merits  of  different 
foundations  ;  the  quality  of  stone  preferable  ;  their  most 
advantageous  size  and  shape ;  their  arrangement ;  the 
manner  of  laying  them  ;  their  borders  and  curbs  ;  theii 
advantages  ;  and  their  comparison  with  McAdam  roads. 


*  The  following  is  part  of  the  specification  for  the  New  York  pavement : 
"  The  paving  stones  must  be  heavy  and  hard,  and  not  less  than  six  inches 
in  depth,  nor  more  than  ten  inches  in  any  direction.  Stones  of  similar 
size  are  to  be  placed  together.  They  are  to  be  bedded  endwise  in  good 
clean  gravel,  twelve  inches  in  depth.  They  shall  all  be  set  perpendicularly 
and  closely  paved  on  their  ends,  and  not  be  set  on  their  sides  or  edges  in 
any  cases  whatever." 

t  The  cost  of  such  a  pavement  for  a  new  street  is  in  New  York  from 
50  to  75  cents  per  square  yard ;  for  repairing  an  eld  street,  about  20  cents 


218  IMPROVEMENT    OF   THE    SURFACE. 


FOUNDATIONS. 

Tl»e  want  of  a  proper  foundation  is  one  of  the  most 
frequent  causes  of  the  failures  of  pavements.  A  founda- 
tion should  be  composed  of  a  sufficient  thickness  of  some 
incpmpressible  material,  which  will  effectually  cut  off 
all  connection  between  the  subsoil  and  the  bottom  of  the 
paving-stones,  and  should  rest  upon  a  well-drained  bot- 
tom, for  which  in  cities  a  perfect  system  of  sewerage  is 
indispensable.  The  principal  foundations  are  those  of 
sand,  of  broken  stone,  of  pebbles,  and  of  concrete. 

Foundations  of  sand. — This  material,  when  it  fills  an 
excavation,  possesses  the  valuable  properties  of  incompres- 
sibility,  and  of  assuming  a  new  position  of  equilibrium 
and  stability  when  any  portion  of  it  is  disturbed.  To  se- 
cure these  qualities  in  their  highest  degree,  the  sand 
should  be  very  carefully  freed  from  the  least  admixture  of 
earth  or  clay,  and  the  largest  grains  should  not  exceed 
one-sixth  of  an  inch  in  diameter,  nor  the  smallest  be  less 
than  one-twenty-fifth  of  an  inch.  The  bed  of  the  road 
should  be  excavated  to  the  desired  width  and  depth,  and 
be  shaped  with  a  slope  each  way  from  the  centre,  corres- 
ponding with  that  which  is  to  be  given  to  the  pavement. 
This  earth  bottom  should  be  well  rammed,  and  a  layer  of 
sand,  four  inches  thick,  be  put  on,  be  thoroughly  wetted, 
and  be  beaten  with  a  rammer  weighing  forty  pounds. 
Two  other  layers  are  to  be  in  like  manner  added,  and  the 
compression  will  reduce  the  thickness  of  twelve  inches  to 
eight.  The  number  of  layers  should  be  regulated  by  the 
character  of  the  subsoil.  Two  inches  of  loose  sand  are 
to  be  then  added  to  fill  the  joints  of  the  stones,  which  may 
be  now  laid.  The  pressure  of  loads  upon  these  stones  is 
ipread  by  the  incompressible  sand  over  a  large  surface 


STONE    PAVEMENTS.  219 

oi  the  earth  beneath.  This  is  the  favorite  system  in 
France.* 

Foundations  of  broken  stone. — A  bed  is  to  be  excava- 
ted, deep  enough  to  allow  twelve  inches  of  broken  stone 
to  be  placed  under  the  pavement.  A  layer  of  four  inches 
is  first  put  on,  and  the  street  then  opened  for  carriages  to 
pass  through  it.  When  it  has  become  firm  and  consoli- 
dated, another  layer  of  four  inches  is  added  and  worked 
in  as  before  ;  and  finally  a  third  layer  ;  making  in  fact  a 
complete  McAdam  road.  Upon  it  the  dressed  paving- 
stones  are  set.t  This  method,  though  efficient,  is  very 
inconvenient,  from  the  length  of  time  which  it  occupies, 
and  the  difficulty  of  draught  while  it  is  in  progress. 

Foundations  of  pebbles. — Such  a  pebble  pavement  as 
is  described  on  page  217,  resting  itself  on  sand,  gravel,  or 
broken  stones,  has  been  recommended  to  be  adopted  as 
the  foundation  of  the  dressed  bk>ck  pavement,  for  streets 
in  which  there  is  a  great  deal  of  travel.^ 

Foundations  of  Concrete.— Concrete  is  a  mortar  of 
finely-pulverized  quicklime,  sand,  and  gravel,  which  are 
mixed  dry,  and  to  which  water  is  added  to  bring  the  mass 
to  the  proper  consistence.  It  must  be  used  immediately. 
Beton  (to  which  the  name  of  Concrete  is  often  improperly 
given)  is  a  mixture  of  hydraulic  mortar  with  gravel  or 
broken  stone  ;  the  mortar  being  first  prepared,  fine  gravel 
incorporated  with  it,  the  layer  of  broken  stones  subse- 
quently added  to  a  layer  of  it  5  or  6  inches  thick,  and  the 
whole  mass  rapidly  brought  by  the  hoe  and  shovel  to  a 
homogeneous  state.  Three  parts  of  sand,  one  of 
hydraulic  lime,  and  three  of  broken  stone  is  a  good  pro« 
portion.  A  mixture  of  one  part  of  Roman  cement,  one  o/ 

*  Gayffier,  p.  126.  t  Parnell,  p.  117. 

J  Committee  of  Franklin  Institute,  and  Parnell,  p  1 16. 


220  IMPROVEMENT    OF    THE    SURFACE. 

sand,  and  oight  of  stone,  has  also  been  employed  very 
successfully.  Beton  is  much  superior  to  Concrete  for 
moist  localities.* 

The  excavation  should  be  made  fourteen  inches  lower 
lhan  the  bottom  of  the  proposed  pavement,  and  filled  with 
that  depth  of  the  concrete  or  beton,  which  sets  very  rap- 
idly, and  becomes  a  hard,  solid  mass^on  which  a  pave- 
ment may  then  be  laid.  This  is,  perhaps,  the  most 
efficient  of  all  the  foundations,  but  also  the  most  costly  at 
first,  though  this  would  be  balanced  by  its  permanence 
and  saving  of  repairs.  It  admits  of  access  to  subterrane- 
ous pipes  with  less  injury  to  the  neighboring  ^avement 
lhan  any  other,  for  the  concrete  may  be  broken  tnrough 
at  any  point  without  unsettling  the  foundation  for  a  con- 
siderable distance  around  it,  as  is  the  case  with  founda- 
tions of  sand  or  broken  stones  ;  and  when  the  concrete  is 
replaced,  the  pavement  can  be  at  once  reset  at  its  proper 
level,  without  the  uncertain  allowance  for  settling  which 
is  necessary  in  other  cases.  The  blocks  set  on  the  con- 
ciete  are  usually  laid  in  mortar.  We  will  examine  pres- 
ently the  propriety  of  this. 

QUALITY    OF    STONE. 

The  stone  should  be  of  a  kind  which  will  not  wear 
smooth,  but  which  will  always  remain  rough  on  the  sur- 
face. Many  varieties  of  granite  are  of  this  character,  and 
are  therefore  very  suitable.  The  hardest  stones  are  the 
best,  and  their  specific  gravity  is  a  tolerable  test  of  theii 
hardness.  The  hardest  stones  will  also  absorb  but  TJ5 
of  their  volume  of  water ;  tender  ones  will  absorb  -£T. 
The  hardest  stones  also,  when  struck  by  a  hammer,  give 
a  clearer  and  more  ringing  sound  than  soft  ones.  Tender 


»  M*hai«,  p.  40 


STONE    PAVEMENTS.  221 

stones  may  be  made  much  more  durable  by  plunging 
them  in  boiling  bitumen,  which  penetrates  their  pores  and 
prevents  them  from  absorbing  water,  which  is  the  most 
powerful  agent  in  their  disintegration. 

SIZE    AND    SHAPE. 

The  size  of  the  stones  should  be  proportioned  to  the 
number  and  weight  of  the  vehicles  which  will  pass  over 
them,  and  as  each  stone  is  liable  to  have  resting  upon  it 
the  entire  weight  borne  by  one  wheel,  it  should  be  large 
enough  to  sustain  this  weight  without  being  crushed,  or 
depressed.  It  should  also  be  no  larger  than  a  horse's 
hoof,  so  as  to  prevent  any  slipping  upon  its  surface,  even 
where  unbroken  by  joints  ;  but  the  fulfilment  of  the  first 
condition  will  generally  make  this  impossible,  and  the  se- 
lection of  a  proper  quality  of  stone  will  render  it  unneces- 
sary. If  stones  of  different  dimensions  are  admitted,  they 
should  be  assorted,  and  only  those  of  the  same  size  should 
be  used  near  each  other,  or  the  small  ones  will  sink  be- 
low the  rest,  and  the  depressions  thus  formed  will  be  in- 
creased by  every  passing  wheel.  It  is  therefore  very 
desirable  that  they  should  be  uniform  in  size.  Cubes  of 
eight  inches  in  every  direction  seem  to  combine  most  of 
these  requisites.  They  should  be  very  slightly  tapering 
towards  their  lower  ends,  thus  making  them  truncated 
pyramids.*  If  they  are  much  larger  than  this  standard, 
the  weight  of  a  wheel  coming  on  one  end  of  one  of  them, 
will  tend  to  depress  it  and  to  elevate  the  other  end,  so 


*  Blocks  of  this  size  cost  in  Philadelphia  delivered  on  the  street,  $2.75 
per  square  yard  of  surface.  Laying  a  bed  of  gravel  15  inches  deep,  set- 
ting the  stone,  &c.,  cost  50  cents  more,  making  the  entire  cost  of  the 
pavement  03.25  per  square  yard. 


222  IMPROVEMENT    OF    THE    SURFACE. 

that  such  large  stones  would  be  less  firm  than  smallei 
ones. 

Hexagonal  blocks  have  been  suggested,  and  would 
form  a  more  compact  mass  than  those  of  any  other  shape  ; 
but  their  superiority  in  this  respect  would  probably  not 
compensate  for  the  extra  cost  of  cutting  them. 

ARRANGEMENT. 

The  rectangular    stones    may  Fig.  111. 

be  laid  in  continuous  courses 
across  the  road,  but  so  as  to 
."break  joints"  in  the  direction 
of  its  length,  as  shown  in  Fig. 
111.  It  has  been  observed,  how- 


,1,1,1,1,  1,1 


I   III 


ever,  that  when  stones  are  laid,  as  is  usual,  with  their 
joints  parallel  and  perpendicular  to  the  direction  of  the 
road,  they  wear  away  most  rapidly  upon  the  edges  which 
run  across  the  road,  since  these  receive  most  directly  the 
shocks  of  the  wheels,  and  that  the  stones  thus  become 
convex.  To  prevent  this,  and  F'g- ll2- 

to  secure  equal  wear,  they 
should  be  laid  so  that  the  joints 
cross  the  road  obliquely,  ma- 
king an  angle  of  45°  with  the 
axis  of  the  roadway.  One  set 
of  joints  may  be  continuous, 
but  the  others  should  break 
joints,  as  in  Fig.  112. 

Oblong  stones  are  preferred  by  the  French  engineers, 
with  their  upper  surfaces  nine  inches  by  five  and  a  half. 
They  should  be  laid,  (if  not  diagonally)  so  that  their  great 
est  length  is  across  the  street,  their  narrowest  dimension 
being  that  passed  over  by  the  wheels.  They  thus  offer  less 


STONE    PAVEMENTS. 


223 


resistance  to  draught  than  cubical 
blocks,  according  to  the  experi- 
ments of  Morin. 

In  the  steep  streets  of  Genoa 
the  stones  are  laid  in  oblique 
courses,  pointing  up  the  ascent, 
and  meetingal  an  angle  in  the  cen- 
tre. The  continuous  joints,  which 
descend  to  the  right  and  to  the 
left,  facilitate  the  discharge  of  the 
rainwater. 


Fig.  113. 


MANNER    OF    LAYING. 

The  top  surface  of  the  foundation  (of  whatever  mate 
rial  it  may  be)  which  forms  the  bed  for  the  paving-stones, 
"s  to  be  shaped,  as  directed  on  page  50,  sloping  each  way 
from  the  centre,  with  inclinations  ranging  from  1  in  50  to 
1  in  100,  flatter  in  proportion  to  the  smoothness  of  the 
surface.  The  stones  should  be  so  set  that  the  joints  be 
tween  them  will  not  exceed  one  quarter  of  an  inch.  But 
as  they  are  not  cut  regularly  enough  to  touch  on  every 
part  of  their  surface,  some  substance  must  be  interposed 
to  fill  up  the  vacancies,  and  to  enable  them  to  support 
each  other.  Mortar  is  used  for  this  purpose  on  founda 
lions  of  concrete,,  and  even  on  those  of  sand  and  broken 
stone.  Sometimes  gravel  is  put  between  them,  and  a 
grouting  of  lime-water  poured  in.  Iron  chippings  are 
added  to  the  gravel  to  increase  the  adherence.  But  no 
adherent  compound,  such  as  these,  can  resist  the  con- 
tinual vibrations  and  play  of  the  pavement.  Some  other 
substance  should  therefore  be  employed,  which  will 
change  its  position  of  equilibrium,  and  never  cease  to  fill 
up  the  spaces  between  the  stones,  whatever  shocks  they 
15 


224  IMPROVEMENT    OF    THE     SURFACE 

may  receive.  Such  a  substance  is  pure  sand.  The 
quality  necessary  has  been  indicated  on  page  218.  A 
coating  of  an  inch  should  also  be  spread  over  the  stones 
When  the  foundation  is  any  thing  but  concrete,  the  paving 
stones  must  be  rammed,  after  a  certain  portion  has  been 
laid,  with  a  maul  weighing  60  Ibs.,  and  those  which  break 
under  this  must  be  replaced,  and  those  which  sink,  taken 
up  and  reset. 

BORDERS   AND    CURBS. 

When  the  paved  road  forms  the  middle  portion,  or 
causeway,  of  a  wider  road,  with  wings  of  earth  or  broken 
stone  on  each  side  of  it,  its  edges  must  be  supported 
against  the  lateral  thrust  of  the  stones,  by  borders  of  larger 
blocks,  9  or  10  inches  wide,  13  to  18  inches  long,  and  13 
inches  deep.  They  are  laid  as  headers  and  stretchers,  so* 
as  to  form  a  bond  with  the  pavement.  Their  outer  edge 
should  also  have  occasional  projections  into  the  wings,  so 
that  a  rut  may  not  be  there  formed. 

When  the  pavement  is  a  city  street,  the  curb-stones 
should  be  long  blocks.* 
There  should  be  no  gut- 
ter or  other  channel  than 
that   formed,    as   in  the 
figure,  by  the  meeting  of 
the  inclined  pavement  with  the  curb-stone,  which  should 
rise  6  or  8  inches  above  the  pavement,  and  be  sunk  as  deep 
into  the  ground  as  possible.     The  foot  pavements  should 


*  In  the  specifications  for  tho  New  York  pavements,  the  Curb-stones 
tire  required  to  bo  not  less  than  3  feet  long,  5  inches  thic^,  and  20  iuchee 
todo  ;  and  the  Gutter-stones  to  be  not  less  than  three  feet  long,  G  inches 
thick,  and  14  inches  wide 


STONE    PAVEMENTS.  225 

incline  towards  the  street  at  the  rate  of  one  inch  in  ten 
feet,  or  1  in  120.* 

ADVANTAGES. 

The  advantages  of  such  a  pavement  are  its  smoothness 
and  uniformity  of  surface,  enabling  vehicles  to  be  drawn 
over  it  with  ease  to  the  horses,  comfort  to  the  passengers, 
and  but  little  wear  and  tear  of  the  carnages,  which  can 
be  therefore  made  much  lighter  than  at  present.  At  the 
same  time  it  gives  a  good  foothold  to  the  horses  ;  causes 
very  little  noise,  yet  enough  to  warn  the  foot-passengers 
of  the  approach  of  a  vehicle,  and  is  very  easily  cleaned 
of  the  dirt  which  may  collect  upon  it.  It  is  also  very 
durable,  thereby  rendering  unnecessary  the  frequent  stop- 
page of  a  street  for  repairs  ;  and  though  at  first  more 
expensive  than  cobble-stones,  is  finally  far  more  eco- 
nomical. 

PAVED  AND  MoADAM  ROADS  COMPARED. 

McAdam  maintains  that  his  roads  are  preferable  t<» 
pavements,  even  for  the  streets  of  cities.  He  argues  tha; 
they  are  cheaper,  as  requiring  no  more  stone  than  pave- 
ments, admitting  an  inferior  quality,  and  costing  less  for 
repairs ;  and  that  they  give  greater  facility  of  travelling,  and 
cause  less  annoyance  from  dust,  when  properly  swept  and 
watered.  But  experience  in  the  streets  of  London  shows 
the  cost  of  broken -stone  roads  to  be  far  greater  than 
pavements,  to  which  they  are  inferior  in  every  respect.f 
The  result  of  very  full  discussions  at  the  Civil  Engineers' 
Institution  was,  that  a  whin  or  granite  pavement,  of  proper 
form  and  depth,  laid  on  a  sound  bottom,  is  preferable  to 

«  Parnell,  p.  120.  t  Parnell,  p.  126. 


220  IMPROVEMENT    OF    THE    SURFACE. 

any  other  plan  for  carriageways  in  the  metropolis  and 
other  large  cities.  The  objections  to  the  broken-stone 
roads  are  that  they  cannot  resist  the  pressure  caused  by  a 
very  great  intercourse,  being  liable  to  be  thereby  crushed 
and  ground  into  dust,  which  is  easily  converted  into  mud  ; 
that  this  hasty  and  continual  destruction  and  renewal 
would,  in  a  great  city,  prove  intolerably  troublesome  and 
expensive,  while  the  dust  in  dry  weather,  and  the  mud  in 
wet,  would  greatly  incommode  the  intercourse  in  the 
streets,  as  well  as  private  dwellings  and  public  shops. 
The  surface  of  broken  stone  is  also  more  injurious  to  the 
feet  of  horses  than  a  good  pavement,  and  less  easy  for 
their  labor  ;  and  the  expense  of  making  and  maintaining 
I  he  former  would  be  at  least  fifty  per  cent,  more  than  the 
latter.* 

ROMAN    ROADS. 

The  ancient  Roman  roads,  which,  even  at  the  present 
day,  after  the  lapse  of  nearly  two  thousand  years,  may  be 
traced  for  miles,  as  perfect  as  when  .first  constructed, 
were  essentially  dressed-stone  pavements,  with  founda- 
tions of  concrete,  resting  on  sub-pavements.  The  most 
perfect  modern  constructions  thus  appear  to  be  only  im- 
perfect and  incomplete  imitations.  The  direction  and 
length  of  the  intended  road  were  marked  out  by  two 
parallel  furrows,  from  the  space  between  which  the  loose 
earth  was  removed.  The  foundation  of  the  road  (Statu- 
men)  was  composed  of  one  or  two  courses  of  large  flat 
stones,  laid  in  mortar,  a  bed  of  which  was  first  spread 
over  the  earth.  Next  came  a  course  of  concrete  (Rudus) 
formed  of  broken  stones  mixed  with  quicklime,  and 


*  Telford  in  Parnell,  p.  351. 


ROMAN    ROADS.  227 

pounded  with  a  rammer.  If  the  stones  were  freshly 
broken  ones,  three  parts  of  them  were  mixed  with  one  of 
quicklime  ;  if  they  were  from  old  buildings,  two  parts  of 
lime  were  used  to  three  of  the  rubbish.  The  third  course 
(Nucleus)  was  composed  of  broken  bricks,  tiles,  and  pot- 
tery, mixed  with  lime,  which  formed  one-fourth  of  the 
whole.  The  mixture  was  spread  in  a  thin  layer,  and  in  it 
were  imbedded,  so  that  their  top  surfaces  were  perfectly 
level,  the  large  blocks  of  stone  (Summa  crusta)  which 
formed  the  pavement.  These  stones  were  irregular  poly- 
gons, usually  with  5,  6,  or  7  sides,  rough  on  their  under 
side,  but  smooth  on  top,  and  so  perfectly  fitted  together 
that  the  joints  were  scarcely  perceptible.  The  entire 
thickness  of  the  four  strata  was  about  three  feet.  When 
the  road  passed  over  marshy  ground,  the  foundation 
stones  rested  on  a  framework  of  timber,  (made  of  a 
species  of  oak  not  subject  to  warp  or  shrink)  and  to  pro- 
tect this  from  the  lime,  it  was  covered  with  a  bed  of 
rushes  or  reeds,  and  sometimes  of  straw.  On  each  side 
of  the  road  were  paved  footpaths,  and  parapets  ;  with 
stones  at  regular  intervals  for  mounting  on  horseback 
Milestones  marked  the  distances  to  all  parts  of  the  empire 
from  the  Milliarium  aurewn,  a  gilt  column  in  the  Forum 
of  Rome. 

The  HUSK  ravtmetit,  (named  from  its  introducer,)  in  New  York,  is  con- 
structed thus  r — The  street  (Broadway)  is  graded  with  a  crowu  of  7  inches= 
.j'g.  Granite  chips  are  spread  over  this,  and  rammed  down  flush  with  the 
earth.  A  concrete  foundation,  6  inches  thick,  is  formed  in  rectangular 
sections.  It  contains  1  part  of  Roseudale  cement,  2£  parts  of  clean 
coarse  sand,  2£  of  broken  stone,  and  2  of  gravel.  On  it  rest  rectangular 
blocks  of  sieiiitic  granite,  10  inches  deep,  10  to  18  long,  and  5  to  12  wide. 
They  are  laid  diagonally,  at  angles  of  45°  with  the  line  of  the  street,  and 
so  as  to  form  lozenge-shaped  compartments.  Lewis  holes  in  certain 
blocks,  and  iron  plates  under  them,  give  easy  access  to  water  and  gas 
pipes,  permitting  excavations  4  feet  long,  and  3£  wide.  The  contract 
price  in  1849  was  $5.50  per  square  yard  of  pavement. 


228 


IMPROVEMENT    OF    THE    SURFACE. 


5.  ROADS  OF  WOOD. 

The  abundance,  and  consequent  cheapness,  of  wood 
in  our  new  country,  renders  its  employment  in  Road- 
making  of  great  value.  It  has  been  used  in  the  form  of 
logs,  of  charcoal,  of  planks,  and  of  blocks. 


Fig.  115. 


LOO    ROADS. 

When  a  road  passes  over  soft 
swampy  ground,  always  kept  moist 
by  springs,  which  cannot  be  drain- 
ed without  too  much  expense,  and 
which  is  surrounded  by  a  forest,  it 
may  be  cheaply  and  rapidly  made 
passable,  by  felling  a  sufficient 
number  of  young  trees,  as  straight 
and  as  uniform  in  size  as  possible, 
and  laying  them  side  by  side  across 
the  road  at  right  angles  to  its  length. 
This  arrangement  is  well  known 
under  the  name  of  a  "  Corduroy"  road,  of  which  the 
figure  gives  a  top  and  end  view.  Though  its  successive 
hills  and  hollows  offer  great  resistance  to  draught,  and 
are  very  unpleasant  to  persons  riding  over  it,  it  is  never- 
theless a  very  valuable  substitute  for  a  swamp,  which  in 
its  natural  state  would  at  times  be  utterly  impassable. 
But  necessary  and  desirable  as  these  roads  may  be  to 
accomplish  such  an  end  in  the  infancy  of  a  settlement, 
their  retention  upon  a  great  thoroughfare  is  a  disgraceful 
pi-oof  of  indolence  and  want  of  enterprise  in  those  who 
habitually  travel  over  them  ;  though  several  such  instances 
might  be  specified. 


CHARCOAL  ROADS.  229 


CHARCOAL  ROADS. 

A  very  good  road  has  been  lately  made  through  a 
swampy  forest,  by  felling  f.nd  burning  the  timber,  and 
covering  the  surface  with  the  charcoal  thus  prepared. 

"  Timber  from  six  to  eighteen  inches  through  is  cut 
twenty-four  feet  long,  and  piled  up  lengthwise  in  the 
centre  of  the  road  about  five  feet  high,  being  nine  feet 
wide  at  the  bottom  and  two  at  the  top,  and  then  covered 
with  straw  and  earth  in  the  manner  of  coal-pits.  The 
earth  required  to  cover  the  pile,  taken  from  either  side, 
leaves  two  good-sized  ditches,  and  the  timber,  although 
not  split,  is  easily  charred ;  and,  when  charred,  the  earth 
is  removed  to  the  side  of  the  ditches,  the  coal  raked 
down,  to  a  width  of  fifteen  feet,  leaving  it  two  feet  thick 
at  the  centre  and  one  at  the  sides,  and  the  road  is 
completed." 

A  road  thus  made  in  Michigan  cost  $660  per  mile, 
and  is  said  to  be  very  compact  and  free  from  mud  or 
dust.  At  a  season  when  the  mud  on  the  adjoining  earth 
road  was  half  axletree  deep,  "  on  the  coal  road,  there  was 
not  the  least  standing,  and  the  impress  of  the  feet  of  a 
horse  passing  rapidly  over  it  was  like  that  made  on  hard 
washed  sand,  as  the  surf  recedes,  on  the  shore  of  the  lake. 
The  water  was  not  drained  from  the  ditches,  and  yet  there 
were  no  ruts  or  inequalities  in  the  surface  of  the  coal 
road,  except  what  was  produced  by  more  compact  pack- 
ing on  the  line  of  travel.  It  is  probable  that  coal  will 
fully  compensate  for  the  deficiency  of  limestone  and  gravel 
in  many  sections  of  the  west,  and,  where  a  road  is  to  be 
constructed  through  forest  land,  that  coal  may  be  used  at 
a  fourth  of  the  expense  of  limestone." 

Two  such  roads  in  Wisconsin  were  let  by  contract  at 
$1.56  and  $  ..621  per  rod,  or  -$499  and  $520  per  mile. 


PJLANK     ROADS. 

Plan  and  Cross  Section  of  a  Plank  Road. 
Fig.  115.  a. 


Fig.        115,     b 


Fig.  115,  a,  Cross-section. 
Fig.  115,  b,  Plan,  or  Top  View. 

Scale,  10  feet  to  1  inch. 


The  most  valuable  improvement  since  McAdam's,  and 
one  superior  to  his  in  many  localities,  is  the  recent  in- 
vention of  covering  roads  with  planks.  The  first  plank 
road  on  this  continent  was  constructed  in  Upper  Canada 
in  1836.  A  short  piece,  laid  down  experimentally,  gave 
so  much  satisfaction,  as  to  ease  of  travelling,  and  cheap- 
ness of  keeping  in  repair,  that  a  mile  of  it  was  construct- 
ed the  next  year  at  a  cost  of  $2100.  Its  success  caused 
it  to  be  continued.  Since  then  500  miles  have  been 
constructed  in  Canada,  and  more  than  2000  registered 
in  the  State  of  New-York ;  and  probably  several  thou 
sands  more  in  the  other  states  of  the  Union  from  Maine 
to  Texas  and  Wisconsin. 


PLANK    ROADS.  231 

In  the  most  generally  approved  system,  two  parallel 
rows  of  small  sticks  of  timber  (called  indifferently  sleep- 
ers, stringers,  or  sills)  are  imbedded  in  the  road,  three  or 
four  feet  apart.  Planks,  eight  feet  long  and  three  or  four 
inches  thick,  are  laid  upon  these  sticks,  across  them,  at 
right  angles  to  their  direction.  A  side  track  of  earth,  to 
turn  out  upon,  is  carefully  rjraded.  Deep  ditches  are  dug 
on  each  side,  to  ensure  perfect  drainage  ;  and  thus  is 
formed  a  Plank  Road. 

The  benefits  of  covering  the  earth  with  some  better 
material  have  been  indicated  on  page  188,  and  the  pecu- 
liar advantages  of  this  plank  covering  will  be  more  fully 
made  known,  when  we  shall  have  discussed  in  order  the 
various  details  of  construction.* 

LAYING    THEM    OUT. 

The  waste  of  labor  caused  by  unnecessary  ascents  in 
a  road,  has  been  pointed  out  in  the  early  part  of  this  vol 
ume,  (pages  32-36.)  It  was  also  shown  (page  28)  thai 
it  is  profitable  to  the  traveller  to  go  two  or  three  thousand 
feet  around  to  avoid  ascending  a  hill  a  hundred  feet  high  ; 
though  the  cost  of  constructing  the  additional  length  o£. 
road  partially  counterbalances  this  consideration.  It  was 
also  proved  that  the  smoother  the  surface  of  the  road  was 
made,  the  nfore  injurious  proportionally  were  such  as- 
cents. They  are  therefore  especially  objectionable  on 
plank  roads,  which  hold  an  intermediate  place  between 
common  roads  and  railroads.  Some  distinguished  engi- 

*  Hon.  Philo  White's  report  to  the  Council  of  Wisconsin,  February, 
1848,  embodies  a  very  extended  and  systematic  collection  of  information 
on  this  subject.  To  it,  and  to  the  valuable  published  and  obliging  private 
communications  of  Hon.  George  Geddes,  C.  E.,  (who  first  introduced  and 
naturalized  this  improvement  in  the  United  States,)  the  author  is  much 
indebted,  as  also  to  many  other  recent  sources. 


232         IMPROVEMENT  OF  THE  SURFACE. 

neers  have  been  led  astray  on  this  point.  Their  argu- 
ments, if  carried  out  to  their  full  extent,  would  lead  to  the 
construction  of  railroads  also  with  similarly  steep  grades. 
It  is  true,  as  they  state,  that  a  given  load  can  be  drawn 
up  a  much  steeper  hill  on  a  plank  road  than  on  a  com- 
mon one,  the  friction  on  the  former  being  so  much  less, 
but  (as  proven  on  pages  34  and  35,  which  see)  this  will 
lessen  in  an  equally  increased  ratio  the  advantages  of  the 
level  portions  of  the  road.  Let  us  assume  the  resist- 
ance of  friction,  or  "  stick-tion,"  (as  Professor  Whewell 
calls  it,)  on  a  plank  road  to  be  one-third  of  that  on  a  good 
earth  road.  It  will  therefore  be  one-sixtieth  of  the  weight 
carried,  if  that  of  the  earth  be  one-twentieth.  If,  now,  a 
horse  can  draw  one  ton  on  the  level  earth  road,  the  total  re- 
sistance will  be  doubled  when  he  comes  to  a  hill  which  rises 
one  foot  in  going  twenty,  (1  in  20,*)  and  he  will  be  able 
to  draw  only  half  a  ton  up  this  hill,  and  therefore  his  load 
on  the  level  parts  of  the  road  would  be  but  half  a  ton  ; 
for  it  would  be  useless  for  him  to  take  more  to  the  hill 
than  he  could  drag  up  it.  Now  suppose  the  same  road 
to  be  planked,  and  this  hill  to  remain  untouched.  On 
•the  level  portions  the  same  horse  can  now  draw  three  tons, 
by  our  hypothesis.  But  the  hill,  rising  1  in  20,  will  offer  a 
resistance  three  times  as  great  as  does  the  "  stiction"  of 
the  plank  road,  and  the  whole  resistance  in  g&ng  up  it  will 
therefore  be/owr  times  as  great  as  on  a  level.  The  horse 
can  therefore  draw  only  one-fourth  of  his  former  load,  or 
only  three-quarters  of  a  ton,  which  is  consequently  the  limit 
of  his  load  on  the  level.  Thus  then  this  hill  has  brought 
down  the  gain  of  the  plank  road  over  the  earth  to  only  a 
quarter  of  a  ton,  instead  of  two  tons,  which  it  would  be, 
were  the  hill  removed.  Therefore,  in  laying  out  a  plank 
road,  it  is  indispensable,  in  order  to  secure  all  the  benefits 


PLANK  ROADS.  233 

which  can  be  derived  from  it,  to  avoid  or  cut  down  all 
steep  ascents. 

A  very  short  rise,  of  even  considerable  steepness,  may, 
liowever,  be  allowed  to  remain,  to  save  expense  ;  since  a 
horse  can,  for  a  short  time,  put  fortn  extra  exertion  to  over- 
come such  an  increased  resistance  ;  and  the  danger  oi 
slipping  is  avoided  by  descending  upon  the  ear'then  track.* 

A  plank  road,  lately  laid  out,  under  the  supervision  of 
Mr.  Geddes,  between  Cazenovia  and  Chittenango,  N.  Y., 
is  an  excellent  exemplification  of  the  true  principles  of 
roadmaking.  Both  these  villages  are  situated  on  the 
"  Chittenango  creek,"  the  former  being  800  feet  higher 
than  the  latter.  The  most  level  common  road  between 
these  villages  rises,  however,  more  than  1,200  feet  in  go- 
ing from  Chittenango  to  Cazenovia,  and  rises  more  than 
400  feet  in  going  from  Cazenovia  to  Chittenango,  in  spite 
of  this  latter  place  being  800  feet  lower.  It  thus  adds 
one-half  to  the  ascent  and  labor,  going  in  one  direction, 
and  in  the  other,  direction  it  goes  up  hill  one-half  the 
height,  which  should  have  been  a  continuous  descent. 
The  line  of  the  plank  road,  however,  by  following  the 
creek,  (crossing  it  five  times,)  ascends  only  the  necessary 
800  feet  in  one  direction,  and  has  no  ascents  in  the  other, 
with  two  or  three  trifling  exceptions,  of  a  few  feet  in  all, 
admitted  in  order  to  save  expense.  There  is  a  nearly 
perpendicular  fall  in  the  creek  of  140  feet.  To  overcome 
this,  it  was  necessary  to  commence,  far  below  the  falls,  to 
climb  up  the  steep  hill-side,  following  up  the  sides  of  the 
lateral  ravines,  until  they  were  narrow  enough  to  bridge, 
and  then  turning  and  following  back  the  opposite  sides  till 
the  main  valley  was  again  reached.  The  extreme  rise  is 
at  the  rate  of  one  foot  to  the  rod,  (1  in  16£  ;)  and  this  only 

*  The  steeper  the  grade,  the  more  rapid  is  the  wear  of  the  planks,  in  a  very  remark 
able  degree ;  a  foot  in  a  rod  doubling  the  wear  on  a  level. 


234          IMPROVEMENT  OF  THE  SURFACE. 

for  short  distances,  and  in  only  three  instances,  with  a 
much  less  grade,  or  a  level,  intervening.  The  line  passes 
through  a  dense  forest,  which  supplied  :As  material,  being 
cut  into  plank  by  sawmills  erected  in  a  gulf  never  before 
approached  by  a  wheeled  carriage. 


A  single  track  of  plank,  eight  feet  wide,  with  an  earth- 
en turn-out  track  beside  it,  of  twelve  feet,  will  in  almost 
all  cases  be  sufficient.  This  gives  twenty  feet  for  the 
least  width  necessary  between  the  inside  top  lines  of  the 
ditches,  the  width  of  which  is  to  be  added,  making  about 
two  rods  on  level  ground.  If  extra  cuttings  or  fillings  be 
required,  the  width  occupied  by  their  slopes  must  be  add- 
ed to  this.  An  earthen  road  of  eight  feet  wide  on  eacli 
side  of  the  plank  track,  has  sometimes  been  adopted.  The 
New  York  general  plank  road  jaw  fixed  four  rods  (66 
feet)  as  the  least  permissible  width  that  plank  roads  might 
be  laid  out.  This  provision  has  since  been  repealed. 

Wider  plank  tracks  were  at  first  employed.  In  Can- 
ada single  tracks  were  made  from  9  to  12  feet  wide.  But 
it  was  found,  on  the  12-feet  Toronto  road,  after  seven 
years'  use,  that  the  planks  were  worn  only  in  the  middle 
seven  or  eight  feet,  and  that  the  remaining  four  or  five 
feet  of  the  surface  had  not  even  lost  the  marks  of  the  saw. 
One-third  of  the  planking  was  therefore  useless,  and  one- 
third  of  the  expenditure  wasted. 

A  double  plank  track  will  rarely  be  necessary.  No 
one  without  experience  in  the  matter  can  credit  the  amount 
of  travel  which  one  such  track  can  accommodate.  Over 
a  single  track  near  Syracuse,  161,000  teams  passed  in 
two  years,  averaging  over  220  teams  per  day,  and  during 
three  days  720  passed  daily.  The  earthen  turn-out  track 


PLANK  ROADS.  235 

must,  however,  be  kept  in  good  order,  and  this  is  easy,  if 
it  slope  off  properly  to  the  ditch,  for  it  is  not  cut  with 
any  continuous  lengthwise  ruts,  but  is  only  passed  over 
by  the  wheels  of  the  wagons  which  turn  off  from  the 
track,  and  return  to  it.  They  thus  move  in  curves,  which 
would  very  rarely  exactly  hit  each  other,  and  this  travel, 
being  spread  nearly  uniformly  over  the  earth,  tends  to 
keep  it  in  shape  rather  than  to  disturb  it. 

If,  however,  there  is  so  much  travel  that  the  earth  track 
will  not  remain  in  good  order,  then  this  travel  will  pay  for 
the  double  track  which  it  requires.  But  this  should  be 
made  in  two  separate  eight-feet  tracks,  and  not  in  one 
wide  one  of  16  or  24  feet,  as  was  at  first  the  practice. 
On  a  wide  track  the  travel  will  generally  be  near  its 
middle,  and  will  thus  wear  out  the  planks  very  une- 
qually, besides  depressing  them  in  their  centre,  and  ma- 
king the  ends  spring  up,  and  when  it  passes  near  one  end 
that  will  lilt  up,  and  loosen  the  other.  Besides,  when  a 
light  vehicle  wisiies  to  pass  a  loaded  one  moving  in  the 
centre,  as  it  naturally  will,  the  former  will  be  greatly  de- 
layed in  waiting  for  the  other  to  turn  aside,  or  else  will 
have  one  wheel  crowded  off  into  the  ditch.  But  where 
there  are  two  separate  tracks,  the  whole  width  of  one  is 
at  the  service  of  the  light  vehicle.  On  a  sixteen-feet  track 
near  Toronto,  the  planks,  having  become  loose  and  un- 
settled, were  sawn  in  two  in  the  centre,  and  this  imper- 
fect double  track,  even  without  any  turn-out  path  be- 
tween, worked  better  than  in  ts  original  state.  An 
experienced  constructor  slates  that  if  he  were  desired  to 
build  a  road  fifty  feet  wide,  he  would  make  it  in  separate 
eight-feet  tracks. 

The  wide  Irack  of  16  feet  plank  has  sometimes  been 
divided  into  two  of  eighl  feel,  by  spiking  down  scantling 


236         IMPROVEMENT  OF  THE  SURFACE. 

20  feet  long,  and  six  inches  square,  along  the  middle  of 
the  road,  at  intervals  of  100  feet  in  the  clear,  between 
each  scantling.  This,  however,  only  partially  remedies 
the  objections  adduced. 

When  the  ground  is  of  such  a  very  unsettled  and  yield- 
ing nature,  such  as  loose  sand,  marsh,  &c.,  that  a  solid 
turn-out  track  of  earth  cannot  be  made,  planks,  sixteen 
feet  long,  may  be  used,  resting  on  three,  four,  or  five 
sleepers,  crowning  in  the  middle  three  or  four  inches,  and 
the  ends  sprung  down,  and  pinned  to  the  outer  sleepers 


The  importance  of  elevating  a  road-bed  above  the  level 
of  the  adjoining  fields,  and  digging  deep  ditches  on  each 
side,  has  been  already  urged,  (pages  53,  54,)  and  this  is 
a  fundamental  requisite  in  making  a  good  plank  road. 
Employ  the  earth  from  the  ditches,  if  good  material,  re- 
jecting the  sods,  to  raise  the  road-bed.  Give  the  ditches 
free  outlets,  cut  their  bottoms  with  true  slopes,  make  under- 
drains,  of  cobble-stones  and  brush,  across  the  road  in  wet 
places,  and  use  every  precaution  to  ensure  thorough  and 
complete  drainage.  This  will  be  more  difficult  in  a  flat 
than  in  a  hilly  country.  If  it  be  effected,  however,  the 
plank  will  last  much  longer,  and  the  road  be  always  in 
better  condition.* 

The  "  cross-section"  of  the  road-bed,  or  its  shape  cross 

*  The  ditches  and  side  slopes  of  the  road-bed,  after  being  ploughed  up, 
may  be  most  rapidly  shaped  by  the  use  of  a  scraper  of  this  form,  3>, 
composed  of  two  planks  hinged  together  in  front,  and  kept  apart  in  the 
rear  by  an  adjustable  cross-piece.  The  team  is  attached  to  the  outer 
plank  at  such  a  distance  from  the  point  as  to  keep  the  inner  plauk  in  the 
direction  of  the  road,  so  that  it  forms  the  straight  edge  of  the  bank,  while 
the  skew  of  the  outer  plank  throws  the  earth  to  one  side  in  the  manner 
of  a  snow-plough,  A  man  with  a  long  lever  inserted  in  the  outer  side 
regulates  this  more  exactly 


PLANK  ROADS.  237 

wise,  between  the  ditches,  must  be  carefully  adjusted  so 
as  to  freely  carry  off  the  rain  which  may  fall  on  it.  First 
decide  on  which  side  of  the  road  the  plank  track  is  to  be 
laid.  It  should  generally  be  on  the  right-hand  side  com- 
ing from  the  country  into  a  town,  so  that  the  farmers' 
wagons  may  keep  upon  it,  when  they  bring  in  their  heavy 
produce,  and  that  the  turning  out  may  be  done  by  those 
which  are  going  back  light.*  The  twelve  feet  width  in- 
tended for  the  earth  track  should  be  heavily  rolled  or  beat- 
en, to  make  it  firm  and  hard.  It  should  slope  down  from 
the  centre  three-quarters  of  an  inch  to  the  foot,  (1  in  16,) 
and  the  eight  feet  of  plank  should  fall  off  three  inches,  or 
1  in  32.  From  each  side  of  the  20  feet  thus  graded,  the 
bank  should  slope  down  to  the  bottom  of  the  ditches  at 
the  rate  of  three  inches  to  the  foot,  or  1  in  4.  (See  Fig. 
115,  a;  page  230.) 

The  proper  shape  may  be  most  easily  and  accurately 
given  by  the  use  of  a  common  mason's  level,  having  a 
tapering  piece  of  wood  under  it,  (as  shown  in  Fig.  88, 
page  173,)  or  having  one  leg  so  much  longer  than  the 
other,  as  will  give  the  slope  required.  If  the  plank  be 
laid  on  an  old  roadway,  no  more  of  it  should  be  broken 
up  than  is  absolutely  necessary  for  imbedding  the  sleep- 
ers, as  it  is  very  desirable  to  preserve  as  solid  a  founda 
tion  as  possible. 

SLEEPERS,  SILLS,   OR  STRINGERS. 

Material. — Pine,  hemlock  tamarack,  oak,  and  walnut, 
have  been  used  in  Canada.  Hemlock  has  been  mostly 
used  in  New  York,  from  its  abundance  and  cheapness 
Pine  would  be  more  durable. 

Number  and  size. — At  first,  five  or  six,  each  six  inches 
square,  were  placed  under  16  feet  plank.  The  Canada 

*  But,  in  ascending  a  long  hil]  in  either  direction,  it  should  be  on  the  right 
'mm!  side. 


238          IMPROVEMENT  OF  THE  SURFACE. 

Board  of  Works'  Specification,  1845,  directs  four  to  be 
put  under  a  16-feet  road,  and  three  under  a  10-feet  road; 
the  outer  ones  to  be  five  inches  square,  and  the  inner  ones 
to  be  six  inches  wide,  and  two  inches  thick,  laid  flatwise. 
On  the  New  York  roads  of  eight  feet  planks,  two  sleep- 
ers, four  inches  square,  have  been  generally  employed. 
They  have,  however,  been  found  insufficient,  and  the  ex- 
perienced engineer  of  the  original  Syracuse  road,  strongly 
recommends  sleepers  12  by  3,  laid  on  their  flat  sides,  and 
for  an  important  road  would  make  them  12  by  4,  or  even 
12  bv  6.*  They  should  be  large  and  strong  enough  to 
hold  up  the  plank  road  in  case  of  a  soft  place  for  a  few 
feet.  Others  argue,  however,  that  they  should  be  small 
enough  to  sink  down  with  the  earth  as  it  settles  under  the 
planks,  so  thalthesemay  continue  to  bear  upon  the  ground ; 
as  otherwise  the  planks  would  be  rapidly  worn  out  by  the 
springing  thus  caused,  and  would  be  soon  rotted  by  the 
confined  air  under  them.  They  also  assert  that  the  only 
use  of  the  sleepers  is  to  keep  the  road  in  shape  when  first 
laid  down.  Indeed,  a  road  three  miles  long  has  been  laid 
in  Canada,  without  any  sleepers  at  all  under  the  planks 
and  it  worked  quite  well.  Its  advocates  say  that  sleepers 
form  a  trench  in  which  water  collects,  and  is  by  them  pre- 
vented from  running  off.  It  therefore  floats  the  planks,  or 
washes  out  mud  from  under  them,  and  thus  forms  a  cav- 
ity, which  produces  the  bad  effects  above  mentioned.  This 
consideration  would  make  light  sleepers  appear  to  be  worse 
than  none.  The  conclusion  seems  to  be  that  large  sleep- 
ers should  be  used  for  an  important  road  ;  and  that  for  a 
poor  one,  which  expects  to  receive  only  light  loads,  and 
which  runs  over  a  hard  bottom,  sleepers  might  perhaps 
be  altogether  dispensed  with . 

*  The  lower  sleeper  may  be  14  inches  wide,  and  the  other  10,  as  the  former  acts 
HB  a  bridge  over  the  channuls  made  under  it  to  let  off  the  water ;  and  also  sustains  a 
somewhat  larger  share  of  the  weight. 


PLANK  ROADS.  23y 

Length. — The  sleepers  used  should  be  as  straight  and 
true  as  possible.  On  the  Syracuse  road  none  less  than 
13  feet  long  were  admitted.  On  the  Canada  roads  they 
are  required  to  be  not  less  than  16  feet,  nor  more  than  20 
feet  long. 

Laying. — Their  distance  apart,  centre  to  centre,  should 
be  such  that  the  wheels  of  loaded  wagons  may  pass  di- 
rectly over  their  middle  ;  or  somewhat  nearer  to  their 
outer  than  their  inner  sides.  This  distance  will  therefore 
vary  in  different  sections  of  the  country,  according  to  the 
usual  "  track"  of  wagons.*  If  this  principle  be  varied 
from,  it  should  be  by  bringing  the  sleepers  nearer  the 
middle  than  the  ends  of  the  planks,  to  prevent  any  de 
pression  in  the  centre.  The  foot-wide  sleepers  in  the 
figure  are  drawn  three  feet  apart  in  the  clear,  or  four  feet 
centre  to  centre. 

They  should  be  well  bedded  in  the  earth,  in  trenches 
cut  to  receive  them,  with  their  top  surface  barely  in  sight. 
They  should  bear  firmly  and  evenly  throughout  their 
whole  length,  and  the  earth  between  them  be  well  ram- 
med down,  and  made  firm,  solid,  and  even.f  The  sleeper 
nearer  the  ditch  is  to  be  laid  so  much  lower  than  the 
inner  one,  as  to  give  the  proper  slope  to  the  road, 
which  is  so  important  for  carrying  off  the  rainwater. 

Joints. — At  the  joints,  where  two  sleepers  come  to 
gether,  end  to  end,  they  are  liable  to  sink  under  passing 
loads.  To  prevent  this,  various  means  may  be  employed, 

*  The  common  track  of  wagous,  measured  "  from  inside  to  outside," 
which  is  the  same  as  from  centre  to  centre,  is  four  feet  eight  inches  in  the 
state  of  New  York.  In  New  Jersey  and  the  Southern  States,  it  is  five  feet. 
In  Connecticut  it  varies  from  three  feet  eight  inches  for  light  wagons,  to  five 
feet  two  inches  for  heavy  ones.  In  Wisconsin,  it  is  five  feet  four  inches. 

t  A  wooden  roller,  weighing  two  tons,  has  been  very  successfully  used 
for  settling  the  sleepers  and  the  earth  between  them,  being  drawn  over 
them  several  times  before  they  are  planked. 


240  IMPROVEMENT  OF  THE  SURFACE. 

The  broad  sleepers  (12  by  3)  may  be  sawn  in  two  length- 
wise, so  as  to  be  each  6  by  3,  and  laid  side  by  side,  so  as 
to  "  break  joints ;"  the  joints  of  one  set  being  opposite 
the  middle  of  the  adjoining  pieces,  which  form  the  other 
set.  This  arrangement  is  shown  in  Fig.  115,  b,  page  230. 
The  sawmills  charge  no  more  for  the  sleepers  in  two 
pieces,  each  6  by  3,  than  in  one  12  by  3.  A  second 
remedy  is  to  lay  a  Fig.115,Cj  ^—  — p-  — ^ 

sliort  board  under  the  ~^ r.  ^-^""Ha-i -^ 

joints  of  the  sleepers,    (       ( 

as  shown  in  Fig.  115,  '     ^          ^  ^ 

c.  A  third  is  to  con- 
nect the  ends  by  a 
mortice  and  tenon,  two 
inches  long,  as  in  Fig.  115,  d.  A  fourth  is  to  unite  them 
by  a  bevel  scarfing,  three  inches  in  length,  reversed  on 
each  half,  as  shown  in  Fig.  115,  e,  in  which,  for  distinct- 
ness, the  two  sleepers  are  represented  as  separated.  In 
every  case  the  joint  on  one  side  of  the  road  ought  to  be 
opposite  the  middle  of  the  sleeper  on  the  other  side 


Material. — In  Canada,  pine,  hemlock,  tamarack,  oak, 
and  walnut,  have  been  employed.  In  this  State,  hemlock 
alone  has  been  used,  being  the  cheapest  material  to  be 
obtained.  Its  defects  are  its  perishable  nature,  and  its 
numerous  knots,  "which  soon  make  the  road  rough,  when 
the  softer  portions  of  the  planks  have  worn  away.  Pine, 
oak,  maple,  or  beach,  would  be  preferable.  In  Wiscon 
sin,  &c.,  white  and  burr  oak  are  abundant,  and  would 
therefore  be  advantageously  used.  Oak  would  make  the 
most  permanent  road,  from  its  superior  capabilities  of  re 
sisting  both  wear  and  decay.  From  its  greater  weight  it 


PLANK  ROADS.  241 

\vould  cost  a  little  more  for  hauling  and  handling.  The 
slipperiness  of  hardwood  has  been  made  an  objection  to 
it,  but  the  sand  with  which  the  road  should  be  covered, 
would  obviate  this.  Whatever  sort  of  limber  is  em 
ployed,  it  should  be  sound,  and  free  from  sap,  bad  knots, 
shakes,  wanes,  or  any  other  imperfections.  The  plank 
should  be  full  on  the  edges,  and  not  less  than  nine  nor 
more  than  sixteen  inches  wide,  if  of  soft  wood,  or  not  more 
than  twelve,  if  of  hard  wood. 

Thickness. — The  planks  are  usually  either  three  or  four 
inches  thick ;  but  the  builders  of  the  later  roads  prefer 
giving  less  strength  to  the  plank,  and  more  to  the  sleep- 
ers, which  are  more  durable  ;  and  therefore  recommend 
three-inch  plank,  with  sleepers  a  foot  wide.  With  hem- 
lock plank,  any  thickness  beyond  three  inches  is  wasted, 
for  when  two  inches  have  been  worn  down,  the  projecting 
knots  will  make  the  road  too  rough  to  travel  on,  and  it 
will  require  renewal.  One  inch  more  will  be  sufficient  to 
hold  the  knots  in,  so  that  we  get  three  inches  as  the  prop- 
er thickness.*  With  less  knotty  timber,  thicker  plank  may 
be  used,  provided  there  will  be  travel  enough  to  wear  out 
the  whole  thickness  from  above,  before  it  unprofitably  rots 
out  from  below.  When  two  tracks  are  laid,  that  which 
would  be  travelled  by  the  loaded  wagons  going  to  market 
may  be  laid  with  four-inch  plank,  and  the  other  track,  for 
the  light  wagons,  with  three-inch  plank. 

Laying. — The  planks  should  be  laid  directly  across  the 
road,  at  right  angles,  or  "  square,"  to  its  line,  as  shown  in 
Fig.  115,  b,  on  page  230.  The  ends  of  the  planks  are 
not  laid  evenly  to  a  line,  but  project  three  or  four  inches 
on  each  side  alternately,  so  as  ^o  prevent  a  rut  being 
formed  by  the  side  of  the  plank  track,  and  to  make  it 
easier  for  loaded  wagons  to  get  upon  it ;  as  the  wheels, 

•  The  knots  niav.  however,  be  cheaply  dubbed  down  with  an  adze. 


242         IMPROVEMENT  OF  THE  SURFACE. 

instead  of  scraping  along  the  ends  of  the  planks,  when 
comiog  towards  the  track  obliquely  after  turning  off,  will 
on  coming  square  against  the  edge  of  one  of  these  pro- 
jecting planks,  rise  directly  upon  it.  On  the  Canada  roads, 
every  three  planks  project  three  inches  on  each  side  of 
the  road  alternately,  as  shown  in  Fig.  115,  b 

The  planks  were  laid  lengthwise  of  the  road,  on  the 
first  one  running  from  Quebec,  it  being  supposed  that  they 
would  wear  better,  and  could  be  more  easily  taken  up  and 
replaced.  But  it  was  found  that  loaded  horses  slipped 
upon  them,  (the  longitudinal  direction  of  the  grain  giving 
no  hold  to  the  feet,)  that  ruts  were  soon  worn  in  them, 
and  that  they  did  not  keep  their  places.  This  arrange- 
ment is  therefore  now  abandoned. 

The  planks  have  also  been  laid  obliquely,  diagonally,  or 
"  skewing ;"  so  as  to  make  an  angle  of  45  degrees  with 
the  ]\ne  of  the  road,  twelve  feet  plank  making  an  eight- 
feet  wide  road.  This  plan  is  adopted  on  the  Longeuil 
ajjd  Chambly  road  near  Montreal.  Its  advantages  are, 
that  the  edges  of  the  plank  are  not  worn  down  so  soon  as 
when  the  wheels  strike  them  directly,  (as  was  shown  :n 
reference  to  pavements,  on  page  222  ;)  that  the  zigzag 
ends  of  the  plank  facilitate  the  getting  on  the  track  ;  and 
that  there  is  less  loss  on  the  rejected,  or  "  cull"  planks  of 
12  feet,  than  on  those  of  8  feet.  But  when  a  wagon- 
wheel  comes  upon  one  end  of  a  plank  laid  thus  obliquely, 
the  other  end,  having  no  load  to  keep  it  down,  will  spring 
up,  if  not  fastened  to  the  sleeper  ;  and  if  it  is,  the  spikes 
or  pins  will  finally  be  loosened.  Each  end  of  each  plank 
undergoes  this  action  in  turn,  and  thus  the  road  is  injured 
.ind  broken  up.  The  first  method  of  laying  the  planks — 
at  right  angles  to  the  direction  of  the  road — is  much  to 
be  preferred. 


PLANK  ROADS  243 

The  planks  must  be  laid  so  as  to  bear  equally  on  the 
sleepers,  and  on  the  ground  between  them,  depending 
chiefly  on  the  latter  for  their  support.  The  earth  must 
be  well  up  to  and  touching  the  planks  at  every  point,  for 
if  any  space  of  confined  air  be  left,  dry  rot  soon  'follows 
If  any  water  be 'allowed  to  get  under  the  planks,  it  forms 
a  soft  mud,  which  is  pressed  up  between  them,  and  de 
posited  on  their  surface,  thus  excavating  a  cavity  under 
them,  and  rendering  them  liable  to  move  under  passing 
loads  in  a  manner  which  soon  wears  them  out.  They 
must  also  be  laid  to  close  joints.* 

Fastening. — On  the  Canada  roads  the  planks  have 
generally  been  spiked  or  pinned  down  to  the  sleepers. 
The  specification  of  the  Board  of  Public  Works  directs 
them  to  be  spiked  "  with  one  spike  at  each  end  for  planks 
1 2  inches  wide  or  less,  and  two  at  each  end  for  planks  of 
a  greater  width.  The  spikes  are  to  be  of  the  description 
called  '  pressed'  spikes,  made  of  the  best  English  or  Ca- 
nadian iron.  They  are  to  be  6^  inches  long,  £  inch 
square,  with  chisel-shaped  edges,  and  good  broad  heads, 
and  are  to  weigh  five  to  a  pound.  They  are  to  be  driven 
with  the  chisel-edge  across  the  fibres  of  the  wood." 

On  the  New  York  roads  this  has  been  considered  an 
unnecessary  expense,  since  the  loads  come  equally  upon 
both  ends  of  the  transverse  planks,  and  thus  tend  to  keep 
them  down  in  their  places,  their  own  weight  assisting  in 
this.  But  in  wet,  and  badly-drained  places,  a  new  con- 
.sideratian  intervenes.  If  the  planks  are  not  fastened  down, 
they  will  float  as  soon  as  an  inch  of  water  gets  under 
them.  The  wheels  of  a  loaded  wagon  pressing  down 
each  plank  in  turn,  drive  the  water  before  them,  till  it 
finally  attains  force  enough  to  throw  up  a  plank,  and  thus 
break  up  the  road.  On  the  other  hand,  when  the  planks 

•  Never  allow  the  eat  h  on  the  sides  of  the  track  to  rise  above  tr\r  ends  of  the  plank 


244         IMPROVEMENT  OF  THE  SURFACE.      • 

are  fastened  down,  the  whole  road  is  floated,  and  the  vi- 
brations produced  by  the  passing  loads  drive  the  water  out 
on  the  sides  and  top  of  the  road,  and  excavate  cavities, 
which  ought  to  be  immediately  filled  up,  an  operation 
which  is  made  difficult  by  the  fastening  down  of  the  planks 
to  the  sleepers.  It  is  therefore  thought 'better  to  leave 
the  plank  free,  and  allow  them  to  be  thrown  out  of  place, 
and  thus  at  once  give  free  passage  to  the  water,  and  pre- 
vent further  mischief;  a  repairer  being  kept  constantly  at 
work  upon  the  road,  and  required  in  rainy  weather  to  pass 
over  every  portion  of  it  once  or  twice  a  day.  It  might  be 
well,  as  a  compromise,  to  spike  down  planks  at  short  in- 
tervals, say  every  fifth  or  tenth  plank,  the  rest  being  well 
driven  home  against  these. 

Covering. — The  planks  having  been  properly  laid,  as 
has  been  directed,  should  be  covered  over  one  inch  in 
thickness,  with  very  fine  gravel,  or  coarse  sand,  from 
which  all  stones,  or  pebbles,  are  to  be  raked,  so  as  to 
leave  nothing  upon  the  surface  of  the  road,  that  could  be 
forced  into  and  injure  the  fibres  of  the  planks.  The  grit 
of  the  sand  soon  penetrates  into  the  grain  of  the  wood, 
and  combines  with  the  fibres,  and  the  droppings  upon  the 
road,  to  form  a  hard  and  tough  covering,  like  feit,  which 
greatly  protects  the  wood  from  the  wheels  and  horses' 
shoes.  Sawdust  and  tan-bark  have  also  been  used. 

The  road  is  now  ready  for  use. 


The  chief  items  in  the  cost  of  a  plank  road  are  the  tim 
her  and  the  earth- work.  The  price  of  the  former  will 
vary  greatly  in  different  localities  and  at  different  times. 
The  cost  of  the  latter,  as  well  as  of  bridges,  culverts,  &c., 
will  generally  be  different  on  eve-y  mile  of  road.  The 


PLA.NK  ROADS.  245 

cost  of  plank  roads  in  general,  therefore,  cannot  be  defi- 
nitely stated.  The  following  estimate  gives  the  extremes. 
On  the  plan  recommended,  the  planking  will  require, 
per  mile,  8  x  3  x  5280  =  126,720  feet ;  and  the  sleepers 
(2)  XI  X3  x  5280  =  31, 680  feet;  in  all  158,400  feet; 
or,  say,  160,000  feet,  board  measure.  Shaping  the  road- 
bed, and  laying  the  sleepers  and  planking,  costs  from  30 
cents  to  $1  per  rod,  according  as  the  line  is  new,  or  on  an 
old  bed,  and  the  soil  easy  or  hard  to  work.  The  number 
of  gate-houses  will  be  governed  by  the  opposing  consider 
ations  of  making  them  many,  so  that  no  one  can  travel  far 
on  the  road  without  paying  therefor  ;  and  few,  so  that  the 
expenses  of  collection  may  be  small.  By  the  New  York 
Plank  Road  raw,  the  toll-gates  are  not  to  be  within  three 
miles  of  each  other.  The  item  of  Contingencies  will  not 
bear  any  relation  to  the  varying  cost  of  the  plank,  and 
therefore  should  not  be  estimated  by  a  percentage,  as  is 
usually  done  These  points  being  premised,  we  arrive 
at  the  following  estimate  of  Cost  per  mile  : 

Plank  :  160  M.  ;  $4  to  $10  per  M.;              .  $640  to  $1600 

Shaping  and  Laying;  30  cents  to  $1  per  rod,  96    "       320 

Gate-houses  :  per  mile 50   "       150 

Engineering  and  superintendence,        .         .  100    "       100 

Contingencies, 100   "       200 

$986  to  $2370 

We  thus  see  that  the  cost  per  mile  will  range  from,  say, 
$1000  to  $2400,  exclusive  of  extra  earth-work,  bridges, 
culverts,  &c.  From  10  to  15  cents  per  cubic  yard  may 
be  estimated  as  the  cost  of  the  excavation,  including  put- 
ting it  into  embankment,  except  when  carried  over  one  or 
two  hundred  feet,  (see  page  132;)  and  it  should  be  stip- 
ulated that  no  cutting  of  less  lhan  two  feet  depth,  should 


240         IMPROVEMENT  OF  THE  SURFACE. 

be  counted,  or  paid  for,  as  "  excavation ;"  but  be  con- 
sidered as  included  in  the  general  price  for  laying.  In 
making  a  new  road  through  a  forest,  the  clearing  and 
grubbing  will  be  a  new  item  of  expense.  Add  ten  per 
cent,  upon  the  cost  of  these  items  for  contingencies  inci- 
dent to  them.  The  land  is  supposed  to  be  given. 

The  Syracuse  and  Central  Square  plank  road,  16 
miles,  cost  $1487  per  mile,  with  lumber  at  $5.20  per  M. 
It  has  a  single  eight-feet  track,  except  over  a  few  spots  of 
yielding  sand.  The  Rome  and  Oswego  road,  62  miles, 
cost  $80,000,  or  about  $1300  per  mile  ;  lumber  costing 
from  $4  to  $5  per  M.  It  is  of  eight  feet  hemlock  plank, 
three  to  four  inches  thick  ;  with  grades  cut  down  to  1  in 
20  near  Rome,  and  at  the  western  end,  where  it  is  more 
hilly,  to  1  in  16^.  'The  Utica  northern  road,  22  miles, 
rost  $42,000,  (besides  $8000  for  right  of  way  over  a  turn- 
pike,) being  nearly  $2000  per  mile,  five  miles  being  a  new 
line  cut  through  woods,  at  an  extra  cost  for  clearing,  of 
$500  per  mile.  Deduct  this,  and  the  average  cost  would 
be  about  $1800  per  mile.  A  short  road  near  Detroit, 
eight  feet  wide,  laid  on  a  travelled  roadway,  cost,  with 
lumber  at  $6  per  M.,  $1500  per  mile. 

The  first  New  York  road  (Syracuse  and  Central 
Square)  was  not  built  by  contract,  but  by  days'  work,  so 
as  to  ensure  the  perfect  bedding  of  the  timbers.  It  was 
also  found  that  the  work  was  done  at  a  less  cost  than  the 
bids  of  contractors,  who  made  such  offers  as  would  se- 
cure them  against  loss  in  a  work  then  new  and  untried. 
In  a  road  where  there  was  much  earthwork,  that  at  least 
should  be  let  by  contract.  The  road  should  also  be  divided 
mto  quarter-mile  sections,  and  the  lumber  for  each  be 
contracted  for,  to  be  equally  distributed  along  the  line, 
when  delivered  The  actual  laving  upon  the  graded  bed 


PLANK  ROADS.  247 

could  then  be  done  by  days'  work.  All  the  operations 
should  be  under  the  charge  of  an  intelligent  and  efficient 
engineer. 

DURABILITY. 

A  plank  road  may  require  renewal,  either  because  it 
has  been  worn  out  at  top  by  the  travel  upon  it,  or  because 
it  has  been  destroyed  at  bottom  by  rot.  But,  if  the  road 
have  travel  enough  to  make  it  profitable  to'  its  builders,  it 
will  wear  out  first ;  and  if  it  does  so,  it  will  have  earned 
abundantly  enough  to  replace  it  twice  over,  as  we  shall 
see  presently.  The  liability  to  decay  is  therefore  a  sec 
ondary  consideration  on  roads  of  importance. 

Wear. — The  actual  wear  is  of  course  proportioned  to 
the  amount  of  travel.  The  most  definite  results  have 
been  obtained  on  the  first  New  York  road,  that  from  Syr- 
acuse to  Central  Square.  In  its  first  two  years,  ending 
July,  1848,  more  than  160,000  teams  passed  over  its  first 
eight  miles.  This  travel  wore  its  hemlock  plank  down 
one  inch,  where  they  had  not  been  floated.  Another  inch 
could  be  worn  down  before  the  projections  of  the  knots 
would  make  it  necessary  to  relay  the  road,  so  that  it 
would  have  borne  the  passage  of  320,000  teams.  But 
tliis  is  an  under-estimate,  inasmuch  as  the  wear  and  tear 
of  the  first  year  is  more  than  that  of  several  following ; 
since  the  first  travel  upon  the  road  tears  off  the  outer 
splinters  and  fibres  cross-cut  by  the  saw,  while  the 
coating  subsequently  formed  protects  the  plank  from 
wear.  Upon  a  Canada  pine  road,  travelled  over  by  at 
least  150  two-horse  teams  per  day,  (50,000  per  year.)  the. 
road  had  worn  down  in  two  years  only  one-quarter  of  an 
inch  ;  and  this  too  was  attributed  chiefly  to  its  exposure 
the  first  year  without  sanding.  It  was  estimated  that 


248         IMPROVEMENT  OF  THE  SURFACE. 

sanded  plank  on  this  road  would  wear  at  least  ten  years. 
Oak  would  of  course  wear  longer. 

Decay. — As  to  natural  decay,  no  hemlock  road  has-  as 
yet  been  in  use  long  enough  to  determine  how  long  the 
plank  can  be  preserved  from  rot.  Seven  years  is  per- 
haps a  fair  average.  Different  species  of  hemlock  vary 
greatly  ;  and  upland  timber  is  always  more  durable  than 
that  from  low  and  wet  localities.  The  pine  roads  in 
Canada  generally  last  about  eight  years,  varying  from 
seven  to  twelve.  The  original  Toronto  road  was  used 
chiefly  by  teams  hauling  steamboat  wood,  and  at  the  end 
of  five  years,  began  to  break  through  in  places,  and,  not 
being  repaired,  was  principally  gone  at  the  end  of  ten 
years.  Having  been  poorly  built,  badly  drained,  not 
sanded,  and  no  care  bestowed  upon  it,  it  indicates  the 
minimum  of  durability.  Oak  plank  cross-walks  in  De- 
troit, the  plank  being  laid  flat  on  the  ground,  have  lasted 
two  or  three  times  as  long  as  those  of  pine.  It  is  be- 
lieved that  oak  plank,  well  laid,  would  last  at  least  12 
or  15  years.  One  set  of  sleepers  will  outlast  two  plank- 
ings ;  several  Canada  roads  have  been  relaid  upon  the 
old  sleepers,  thus  much  lessening  the  cost  of  renewal. 

A  Canadian  engineer  thinks  that  $20  per  mile  would 
be  required  the  first  year  ;  to  restore  the  grade  when 
it  had  settled,  to  fasten  loose  plank,  &c.  For  the  next 
five  years,  $10  per  mile,  and  then  there  would  be  some 
planks  to  be  replaced.  The  repairs  would  then  increase 
so  as  to  amount  to  a  renewal  of  the  surface  at  the 
end  of  four  years  more,  making  ten  for  the  age  of  the 
road, 


PLANK  ROADS.  249 


ADVANTAGES, 


Plank  roads  are  the  Farmer's  Railroads.  He  profits 
most  by  their  construction,  though  all  classes  of  the 
community  are  benefited  by  any  such  improvement, 
as  has  been  fully  shown  in  the  "  Introduction"  to  this 
volume.  The  peculiar  merit  of  plank  roads  is,  that  the 
great  diminution  of  friction  upon  them  makes  them  more 
akin  "to  railroads  than  to  common  roads,  with  the  advan- 
tage over  railroads,  thai,  every  one  can  drive  his  own 
wagon  upon  them.  Their  advantages  naturally  divide 
themselves  into  two  classes  ;  their  utility  to  the  commu- 
nity at  large,  and  their  profits  to  the  stockholders  who 
build  them. 

1 .  To  the  community.  A  horse  can  draw  on  a  plank 
road  from  two  to  three  times  as  much  as  he  can  on  an 
ordinary  Macadam  or  good  common  road.  On  the  latter 
roads  one  ton  is  a  fair  load  for  a  single  horse,  and  3000 
Ibs.  the  utmost  allowance.  But  upon  a  plank  road,  a 
iwo-horse  team  has  drawn  six  tons  of  iron  ;  another  has 
drawn,  for  several  days  in  succession,  over  two  cords  of 
green  beech  and  maple  wood,  estimated  at  six  tons  also, 
and  could  draw  four  or  five  tons,  thirty  miles  a  day  con- 
tinuously. These  results  of  experience  agree  with  the 
calculations  founded  on  the  data  of  p.  62,  taking  the  fric- 
tion on  i  Macadam  road  at  ~-g,  (the  average  of  the  two 
values  there  given,)  and  that  on  planks  at  s\.  The  re- 
sulting ratio  is  2£  to  1. 

A  great  degree  of  speed  can  also  be  obtained  upon 
plank  roads  with  much  less  injury  to  the  vehicles  and  to 
ihe  horses  feet  than  on  a  Macadam  road,  though  contrary 
impressions  have  sometimes  been  caused  by  the  excessive 
speed  with  which  their  light  draught  often  causes  horses 
to  be  driven,  without  the  driver  being  aware  of  it.  Eight 


250 


IMPROVEMENT  OF  THE  SURIA.CE. 


feet  of  a  Canadian  McAdamized  road,  disrupted  by 
frost,  was  taken  up,  and  planked  over ;  and  the  horses 
when  reined  from  the  plank  to  the  stone,  in  turning  out, 
would  of  their  own  accord,  if  not  prevented,  immediately 
turn  back  upon  the  plank. 

But  the  peculiar  advantage  to  the  community  of  plank 
roads  is  their  continuing  in  perfect  order,  and  affording 
undiminished  facilities  for  travel,  at  all  seasons,  while 
common  roads  are  rendered  impassable  by  the  continued 
rains  of  autumn,  the  occasional  thaws  in  mid-winter,  or 
•the  "  breaking  up"  in  spring.  They  thus  enable  the 
farmer  to  carry  his  produce  to  market  at  seasons  and 
in  weather  when  he  would  otherwise  be  imprisoned  at 
home,  and  could  not  there  work  to  advantage.  His  farm 
will  therefore  be  made  more  valuable  to  him  ;  and  it 
has  accordingly  been  found  that  the  value  and  price 
of  lands  contiguous  to  those  roads  have  been  enhanced 
by  their  operation  to  such  a  degree  as  to  excite  the  envy 
and  complaints  of  those  living  off  their  line.  The  les- 
sened "  stiction"  will  also  enable  him  to  carry  his  former 
load  to  a  more  distant  market,  if  desired,  or  to  carry  to 
his  former  market  a  larger  load,  and  therefore  at  less 
cost  per  bushel,  hundred-weight,  or  cord.  He  can  there- 
fore sell  cheaper,  and  yet  gain  more.  The  consumer 
of  his  produce,  wood,  &c.,  gets  a  better  supply  of  all 
articles,  and  at  lower  prices.  The  shopkeepers  carry  on 
an  active  trade  with  their  country  customers,  at  times 
when,  were  it  not  for  these  roads,  they  would  have  noth- 
ing to  do.  It  is  one  of  those  few  business  arrange- 
ments by  which  all  parties  gain,  and  which,  therefore, 
in  the  words  of  Clinton,  actually  "  augment  the  public 
wealth." 


PLANK  ROADS.  251 

2.  To  the  stockholders.  The  annual  profits  of  a 
plank  road  will  of  course  be  governed  by  the  two  ele- 
ments of  its  first  cost,  and  the  amount  of  travel  upon  it. 
The  latter  should  be  approximately  determined  in  ad- 
vance, as  directed  on  page  66.  One  important  point 
has,  however,  been  determined  with  considerable  accu- 
racy, viz.  :  how  much  a  road  will  earn  before  it  is  worn 
out.  Upon  the  first  eight  miles  of  the  Syracuse  and 
Central  Square  plank  road,  the  tolls  during  its  first  two 
years,  ending  July,  1848,  amounted  to  $12,900,  and  the 
expenses  for  salaries  and  repairs  to  $1,500;  leaving 
$11,400  for  dividends  and  rebuilding.  This  amount  of 
travel  had  worn  the  plank  down  one  inch.  Another  inch 
could  be  worn  down  before  a  renewal  would  be  neces- 
sary, and  the  road  would  then  have  earned  $22,800 
above  expenses,  or  $2,850  per  mile.  This  experience 
indicates  that  hemlock  plank  before  being  worn  outs  will 
earn  two  or  three  times  their  original  cost.  The  surplus 
above  the  cost  of  renewal  will  therefore  be  payable  in 
dividends,  amounting  in  gross  to  between  100  and  200 
per  cent,  upon  the  first  cost  of  the  plank,  (that  of  the 
whole  road  bearing  no  constant  ratio  to  this  ;)  the  amount 
of  each  annual  dividend  being  of  course  greater  the  more 
rapidly  this  wearing  out,  with  its  concomitant  and  pro- 
portional earning,  takes  place. 

This  calculation  is  predicated  on  the  tolls  established 
by  the  New  York  Plank  Road  law,  which  are  as  follows  : 
For  any  vehicle  drawn  by  two  horses,  &c.,  1|  cents  per 
mile,  and  £  cent  for  each  additional  animal ;  for  vehicles 
drawn  by  one  horse  £  cent  per  mi.e;  for  a  horse  and 
rider,  or  led  horse,  ^  cent;  for  every  score  of  sheep; 
swine,  or  neat  -attic,  one  cent  per  mile.  But  the  com- 


252          IMPROVEMENT  OF  T'lE  SURFACE. 

panics  are  not  to  charge  more  than  will  enable  them  to 
pay  annual  dividends  of  10  per  cent,  upon  the  stock  actu- 
ally paid  in  and  expended  on  the  road,  after  keeping  the 
road  in  repair,  and  setting  aside  10  per  cent,  for  its  re- 
construction. This  restriction  has  since  been  repealed.* 

The  great  objection  to  plank  roads  in  the  eyes  of  an 
engineer  is  their  perishable  nature,  and  consequent  final 
destruction.  But  this  fault  is  one  not  peculiar  to  plank 
roads,  but  common  to  all  in  a  greater  or  less  degree. 
Thus  in  the  case  of  broken-stone,  or  McAdam  roads, 
usually  cited  as  contrasting  models  of  durability,  we  find 
that  they  wear  away  so  rapidly  as  to  require  not  only  con- 
stant repairs,  but,  when  well  kept  up,  an  actual  addition 
to  their  substance  of  one  cubic  yard  per  mile  for  each 
beast  of  burden  passing  over  them,  (see  page  209;)  and 
the  80,000  teams  per  year  which  passed  o.ver  the  Syra- 
cuse road,  wo*ld  have  required  an  amount  of  broken 
stone,  to  replace  their  wear,  enough  to  renew  it  many 
times  over.  A  Canadian  report  to  the  Board  of  Public 
Works  shows  that  the  cost  of  one  mile  of  McAdam  road 
will  there  make  and  maintain  nearly  four  miles  of  plank 
road  ;  and  on  one  road  the  substitution  of  plank  for  bro- 
ken stone  effected  a  saving  of  an  amount  sufficient  to  re- 
plank  the  road  every  three  years,  if  that  had  been  ne- 
cessary. The  New  York  Senate  report  states  that  a 
plank  road  over  the  same  line  with  a  McAdam  one  can 
often  be  built  and  maintained  for  less  than  the  interest  on 
the  cost  of  a  McAdam  one,  added  to  the  expense  of  its 


*  The  New  York  Laws  relating  to  Plank  Roads,  are  -1847,  chapters 
310,  2S7,  398  :  1848,  chapt.  360  :  1849,  chapt.  250. 


WOODEN  PAVEMENTS.  253 

necessary  annual  repairs.  But  even  if  a  plank  road  was 
still  more  perishable  than  it  is,  and  was  worn  out  in  one 
year,  still,  if  in  that  time  it  had  repaid  its  cost  two  or 
three  fold,  (as  we  have  seen  it  would  do,)  it  would  be  so 
much  the  more  profitable  investment ;  and  this  is  the 
final  object  of  all  private  engineering  constructions. 

It  should  not  be  forgotten  by  the  engineer  engaged  in 
laying  out  a  road  for  a  private  company,  that  their  inter- 
ests, and  those  of  the  public  who  are  to  use  the  road,  are 
not  identical.  The  public  wish  the  road  to  be  so  laid  out 
that  they  can  carry  over  it  the  greatest  possible  loads  at 
the  least  possible  cost.  The  stockholders  generally  wish 
only  to  secure  to  themselves  the  largest  possible  amount 
of  tolls  in  return  for  the  smallest  possible  investment. 
These  two  interests  conflict.  The  steep  ascents,  so  in- 
jurious to  the  travelling  public,  as  shown  on  pp.  231-3, 
are  advantageous  to  the  company  who  plank  the  road, 
since  they  prevent  large  loads  being  carried,  and  thus 
produce  a  twofold  gain — the  amount  of  tolls  being  pro- 
portioned to  the  number  of  the  loads,  and  not  (as  they 
should  be)  to  their  weight ;  and  the  carriage  of  such  ex- 
cessive ones  as  would  break  defective  plank  being  thus 
prevented.  The  engineer  of  the  company  must  therefore 
sacrifice  the  absolute  perfection  of  his  road  to  this  requisi- 
tion of  policy,  and  may  leave  steep  ascents  untouched,  thus 
saving  the  first  cost  of  cutting  them  down,  as  well  as  in- 
creasing the  subsequent  receipts.  But,  on  the  other  hand, 
if  the  grades  of  the  road  be  not  sufficiently  improved,  it 
may  not  attract  the  expected  amount  of  travel.  A  pru- 
dent compromise  must  therefore  be  made  between  these 
opposing  interests 


254  IMPROVEMENT    OF    THE    SURFACE. 

WOODEN  PAVEMENTS. 

Pavements  formed  of  wooden  blocks, 
usually  hexagonal  in  shape,  possess 
many  advantages.  They  cause  little 
resistance  to  draught ;  are  almost  en- 
tirely free  from  noise ;  are  easily 
kept  clean  ;  are  easy  to  a  horse's  hoof; 
lessen  very  much  the  wear  and  tear 
of  vehicles  ;  nre  pleasant  to  travel- 
lers ;  admit  of  great  speed,  and  are  cheaper  in  their  firs 
cost  than  granite  blocks. 

To  counterbalance  these  recommendations,  they  are 
slippery  and  therefore  dangerous  in  wet  weather  ;  and  are 
very  perishable,  both  from  wear  and  from  decay.  The 
slipperiness  has  been  obviated  by  grooving  and  striating 
their  surface,  but  this  lessens  their  ease  of  draught  and 
noiselessness,  and  increases  their  cost.*  The  rapidity  of 
their  wear  may  be  lessened  by  setting  them  on  a  founda- 
tion of  broken  stone,  or  of  concrete,  so  shaped  as  to  rap- 
i^ly  drain  the  water  from  their  bottoms  ;  and  by  covering 
their  surfaces  with  a  mixture  of  boiling  tar  and  clean 
gravel.  Their  decay  may  be  prevented  by  .various  chem- 
ical preservatives,  of  which  the  principal  are,  Ryan's,  who 
saturates  the  wood  with  a  solution  of  bichloride  of  mer- 
cury or  corrosive  sublimate  (one  pound  to  five  gallons  of 
water) ;  Burnett's,  who  uses  a  solution  of  chloride  of  zinc. 
(one  pound  to  ten  gallons  of  water)  absorbed  in  a  vacuum  ; 
Renwick's,  with  coal  tar ;  and  Boucherie's,  with  the  im- 
pure pyrolignite  of  iron,  absorbed  by  the  vital  action  of 
the  sap  vessels. 

*  A  description  of  various  forms  proposed  for  wooden  pavements  may 
be  found  in  the  N.  Y.  American  Repository,  vol.  iii. ;  and  in  London  Me- 
chanics' Magazine,  and  Repertory  of  Patent  Inventions,  passim. 


BOADS    OF    BRICKS,    CONCRETE,    ETC.  255 


0.  ROADS  OF  OTHER  MATERIALS. 
BRICK. 

Roads  are  made  in  Holland  of  hard  burnt  bricks,  or 
"  clinkers,"  laid  on  a  firm  foundation,  and  set  on  edge, 
with  their  longest  dimension  across  the  road.  A  better 
bond  would  be  obtained  by  Fig.  117. 

such  an  arrangement  as  is 
shown  in  the  figure.  But 
the  pressure  of  heavy  loads 
and  the  blows  of  horses' 
feet  are  too  powerful  for 
bricks,  which  should  therefore  be  reserved  for  foot-pave 
ments  only. 

CONCRETE. 

Roads  of  concrete,  or  beton,  six  to  eight  inches  thick, 
(such  as  has  been  described  as  the  best  foundation  for 
granite  blocks)  have  been  warmly  advocated  in  France, 
particularly  for  the  use  of  stearn  carriages,  in  the  place 
of  the  more  costly,  though  more  perfect  railroads.  Con-' 
crete  will  sustain  great  weights,  carried  on  wheels,  with 
little  injury,  but  has  been  found  (on  the  towpath  of  a  ca- 
nal aqueduct)  to  be  rapidly  destroyed  by  the  feet  of 
horses. 

CAST  IRON. 

This  material  has  been  tried  several  times,  but  aban- 
doned in  consequence  of  its  wearing  so  smooth  as  to 
cause  horses  to  slip 

17 


256  IMPROVEMENT    OF    THE    SURFACE. 


ASPHALTTM. 

This  name  has  been  given  to  a  bituminous  mastic,  of 
which  the  principal  localities  are  Seyssel  in  France,  and 
Val-de-travers  in  Switzerland.  A  limestone  is  also  there 
found,  which  contains  from  3  to  15  per  cent,  of  bitumen. 
The  stone  is  broken  into  fragments  of  the  size  of  an  egg, 
and  ground  to  powder.  A  certain  proportion,  usually 
from  6  to  10  per  cent.,  of  mineral  tar  (obtained  by  boiling 
in  water  the  bituminous  sandstone  of  the  same  place)  is 
combined  with  the  limestone,  by  heating  the  former  in 
iron  boilers,  and  gradually  adding  and  stirring  in  the 
powdered  stone.  In  this  state  it  is  poured  upon  a  level 
surface,  and  forms  smooth  cakes,  over  which  gravel  is 
spread.  It  is  too  weak  for  carriage-ways,  and  in  this 
climate  too  soft  in  summer,  and  too  brittle  in  winter,  for 
even  foot-pavements  ;  but  in  Paris  the  asphaltum  side- 
walks of  the  Boulevards  are  most  perfect  specimens  of 
pavements.  The  asphaltum  is  melted  on  the  spot  in 
large  caldrons,  and  poured  within  a  moveable  frame  to  the 
desired  thickness.  The  edges  of  these  slabs  are  united 
with  the  same  material,  and  the  pavement  before  an  en- 
lire  block  of  houses  is  thus  made  one  smooth  level  sur- 
face, unbroken  by  a  single  joint. 

CAOUTCHOUC. 

A  pavement,  formed  by  mixing  gravel  with  melted 
caoutchouc,  or  gum  elastic,  has  been  tried  in  London.  A 
specimen  in  the  court-yard  of  the  Admiralty,  in  1844, 
was  very  pleasant  to  walk  upon,  but  showed  permanent 
depressions  where  heavily  loaded  vehicles  had  passed 
over  it. 


ROADS  WITH  TRACKWAYS.  257 

7.  ROADS  WITH  TRACKWAYS. 

When  wheeled  carriages  are  drawn  by  hoises,  the 
wheels  sbould  move  on  the  smoothest  and  hardest  sur 
face  possible,  while  the  horses  require  one  rough  enough 
to  give  them  a  secure  foothold,  and  soft  enough  to  be 
easy  to  their  feet.  These  two  opposite  requirements  are, 
united  only  in  Roads  with  Trackways,  on  which  two 
parallel  tracks  of  suitable  materials  are  provided  to  re- 
ceive the  wheels,  while  the  space  between  the  tracks  is 
filled  with  a  different  material,  on  which  the  horses  travel. 
The  wheel-tracks  are  usually  of  stone,  of  wood,  or  of  iron. 

STONE    TRACKWAYS. 

The  Egyptians  seem  to  have  first  discovered  the  value 
of  stone  trackways  in  moving  great  weights,  for  traces  of 
such  contrivances  have  been  found  in  the  quarries  which 
supplied  the  enormous  stones  of  their  Pyramids.  In 
modern  times  they. reappeared  in  the  streets  of  Pisa,  and 
are  now  general  in  those  of  Milan.  They  have  of  late 
years  been  used  with  great  advantage  in  London,  upon  a 
road  over  which  250,000  tons  annually  passed,  in  wagons 
carrying  each  five  tons.  The  repairs  of  this  road  for 
thirteen  years  cost  less  than  one  hundred  dollars.  The 
friction  upon  this  stone  trackway  was  so  much  reduced 
(being  only  r\^  of  the  weight)  that  a  small  horse  (weigh- 
ing 4|  cwt.)  could  draw  on  a  level  15  tons  ;  and  a  pow- 
erful horse  ^weighing  14  cwt.)  30|  tons,  at  the  rate  of  4 
miles  per  hour.  On  this  road  the  tracks  were  blocks  of 
granite  5  or  6  feet  long,  16  inches  wide,  and  12  inches 
deep.  The  space  between  them  was  paved.* 

»  Parnell,  p.  106 


IMPROVEMENT  OF  THE  SURFACE. 


A  similar  trackway  of  stone  has  been  used  with  grea 
advantage  to  facilitate  the  ascent  of  a  steep  hill,  as  a  sub 
stitute  for  reducing  the  inclination.  Upon  the  Holyhead 
road,  two  hills,  each  a  mile  in  length,  hud  an  inclination 
of  1  in  20.  To  reduce  this  to  1  in  24  would  have  cost 
$100,000.  Nearly  the  same  advantage,  in  diminishing 
the  tractive  force  required,  was  obtained  by  moderate 
cutting  and  embankment,  and  making  stone  trackways,  at 
a  total  expense  of  less  than  half  the  former  amount.  To 
draw  one  ton  over  the  original  hills  required  a  power  of 
294  Ibs. ;  to  draw  it  over  the  trackways  laid  on  the  same 
inclinations  required  only  132  Ibs. ;  so  that  the  tractive 
force  was  reduced  more  than  one-half  by  this  improve 
ment ;  and  the  effect  was  the  same  as  if  the  hill  had  been 
cut  down  to  a  level,  its  surface  remaining  unchanged 
The  arrangement  of  this  trackway  is  shown  in  Fig.  118 
Fig.  118. 


I  I   I  I  i   r* 


The  blocks  were  of  granite,  twelve  inches  deep,  fourteen 
inches  wide,  and  not  less  than  four  feet  long.*  A  foundation 
for  them  was  prepared  by  making  an  excavation,  8  feet  wide 
and  25  inches  deep.  On  its  levelled  bottom  was  laid  a  rough 
pavement  (like  that  described  for  the  "  Tel  ford  road,"  page 
210)  eight  inches  deep.  The  joints  were  also  filled  with 
gravel.  Upon  this  pavement  were  laid  three  inches  of  broken 
stones,  none  exceeding  one  and  a  half  inches  in  their  longest 


ROADS    WITH    TRACKWAYS.  259 

dimensions,  On  them  was  a  layer  of  two  inches  of  the  best 
gravel,  over  which  a  heavy  roller  was  passed.  Upon  this  the 
stone  blocks  or  "  trams"  were  laid  to  a  very  accurate  level. 
The  spaces  between  and  outside  of  them  were  filled  up  to  a 
depth  of  six  inches  with  broken  limestone.  On  each  side  of 
the  blocks  was  placed  a  row  of  paving-stones  of  granite,  six 
inches  deep,  five  inches  wide,  and  nine  inches  long.  The  re- 
maining space  was  filled  up  with  hard  broken  stone,  and  the 
whole  covered  with  a  top  dressing  of  an  inch  of  good  gravel.* 

WOODEN    TRACKWAYS. 

In  districts  where  timber  abounds,  it  may  be  substituted 
for  stone  in  forming  tracks,  on  which  the  wheels  of  or- 
dinary vehicles  may  run.  Projections  on  the  sides  of  the 
tracks  may  be  employed  to  retain  the  wheels  upon  them, 
but  the  moisture  retained  in  the  joints  would  cause  rapid 
decay,  and  if  any  such  precaution  be  thought  necessary, 
a  furrow  or  gutter  in  one  of  the  tracks  would  be  prefera- 
ble.! It  would  of  course  be  necessary  in  this  case,  that 
the  road  should  everywhere  have  sufficient  inclii  ation  to 
carry  off  the  water,  which  would  otherwise  fill  the 
furrow. 

Fig.  119. 


The  road-bed  should  first  be  properly  shaped,  with  an 
inclination  each  way  from  the  centre,  and  the  timbers  be 
completely  imbedded  in  it.  Two  tracks  should  be  laid, 
for  the  travel  in  the  two  directions.  A  faster  vehicle, 
overtaking  a  slower  one,  could  easily  leave  the  track  and 

*  Parnell,  p.  109. 

t  See  report  of  Mr  Jno.  S.  Williams,  American  Mechanics'  Maga 
»me,  p.  210 


260 


IMPROVEMENT  OF  THE  SURFACE. 


re-enter  it  after  passing.  The  outside  timber  of  each 
track  should  be  smooth  on  its  upper  surface,  and  the 
inner  one  have  hollowed  in  it  a  furrow,  about  3  inches 
deep,  4  inches  wide  at  bottom,  and  twice  that  at  top. 
The  flat  timber  should  be  wide  enough  to  allow  for  the 
usual  variation  in  the  widths  of  vehicles.  The  rise  of  the 
road  between  the  two  timbers  should  just  equal  the  depth 
of  the  furrow,  so  that  the  two  wheels  may  be  on  the 
same  level.  The  distance  between  the  centres  of  the 
timbers  should  be  about  5  feet ;  between  the  two  tracks  a 
space  of  four  feet  should  be  left ;  and  on  the  outside  of 
each,  nine  and  a  half  feet  for  a  summer  road,  making  a 
total  width  of  33  feet,  or  two  rods. 

The  railroad  from  Clifton  to  the  Adirondack  mines, 
New  York,  is  made  of  wooden  rails.  They  are  of  hard 
maple,  6  by  4  inches,  and  14  feet  long.  They  are  set  on 
edge  into  notches  in  the  ties,  and  are  fastened  by  wooden 
wedges. 

IRON    TRACKWAYS. 

The  wooden  tracks,  adopted  more  than  two  centuries  ago 
in  the  coal-mines  of  England,  were  before  long  covered 
with  thin  plates  of  iron  to  increase  their  durability  and  tc 
lessen  their  friction,  and  subsequently  replaced  by  tracks 


entirely  of  iron.  While  a  flange  on 
their  sides  was  used  to  keep  car- 
riages upon  them,  they  were  "  tram- 
roads,"  but  when  the  flange  was 
transferred  from  the  road  to  the  wheel, 
the  trackway  became  a  RAILWAY. 
The  extent  of  this  topic  demands  for 
it  a  separate  chapter. 


Fig.  120 


RAIL-ROADS.  261 


CHAPTER  Y. 

RAIL-ROADS. 

"Nothing  can  do  more  harm  to  the  adoption  of  railroads,  than  the 
promulgation  of  such  nonsense  as  that  we  shall  see  locomotive  engines 
travelling  at  the  rate  of  12,  16,  18,  and  20  miles  per  hour!" 

WOOD,  on  Railroads,  1825. 

"  An  express  train  on  the  Great  Western  Railway,  drawing  59  tons, 
has  travelled,  for  three  hours,  at  the  rate  of  63  miles  per  hour !" 

RITCHIE,  on  Railways,  1846. 

THE  great  success  and  rapid  extension  of  railroads,  are 
due  to  that  appreciation  of  the  value  of  time,  which  is 
the  characteristic  of  the  present  age.  The  speed  obtained 
upon  them  virtually  and  practically  shortens  distances  in 
the  precise  ratio  in  which  it  abridges  the  time  occupied 
in  travelling  over  them. 

The  rapidity  of  motion  and  power  of  traction,  which 
are  attainable  on  railroads,  depend  on  their  diminution  of 
friction.  This  is  the  chief  element  in  the  improvement 
of  the  surface  of  all  roads,  and  in  the  preceding  chapter 
we  have  considered,  in  the  order  of  their  progressive 
merits,  the  various  means  which  may  be  employed  for 
that  object.  In  railroads  we  have  arrived  at  their 
climax. 

The  essential  attributes  of  a  railroad  are  two  smooth 
surfaces,  usually  of  iron,  for  the  wheels  to  run  upon. 
These  surfaces  must  be  made  as  narrow  as  possible,  to 
lessen  their  cost,  and  some  contrivance  to  keep  the  wheels 


iJ62  RAIL-ROADS. 

upon  them  is  then  rendered  necessary ;  the  usual  one  at 
present  being  a  projection,  or  "  flange,"  on  the  inner  rim 
of  the  wheel. 

Since  the  peculiar  wheels,  which  are  the  chief  source 
of  the  superiority  of  railroads,  prevent  the  vehicles  which 
are  adapted  to  run  upon  them,  from  being  used  on  ordinary 
roads,  railroads  pass  out  of  the  practical  scope  of  the 
present  treatise ;  for  the  details  of  their  construction  no 
longer  belong  to  the  community  at  large,  but  demand  the 
highest  professional  skill  of  the  Civil  Engineer.  The 
general  interest,  however,  in  the  subject  of  railroads 
seems  to  demand  some  explanation  of  the  leading  princi- 
ples which  should  govern  those  engaged  in  their  establish- 
ment, and  some  account  of  the  ingenious  contrivances 
which  have  been  adopted  to  overcome  the  difficulties, 
which  have,  one  after  another,  risen  up  in  vain  efforts  to 
stop  the  progress  of  the  giant.  A  brief  popular  view  of 
these  topics  (without  the  minute  practical  details  with 
which  the  subject  of  roads  in  general  has  been  treated) 
will  accordingly  be  given  in  the  present  chapter.* 

Wooden  railways  were  employed  as  a  substitute  for 
common  roads,  in  the  collieries  of  England,  soon  after  the 
year  1600.1  The  earliest  record  of  their  existence  is  in 
the  life  of  the  Lord  Keeper  North,  wherein  it  appears  that 
about  the  year  1670,  they  were  used  at  Newcastle-on- 
Tyne,  for  transporting  coal  from  the  mines  to  the  river, 
and  enabled  one  horse  to  draw  four  or  five  chaldrons. 


*  The  principal  authorities  consulted  have  been  Lecount,  "  Treatise 
on  Railways,"  from  the  seventh  edition  of  the  Encyclopedia  Britannica ; 
Ritchie, "  On  Railways  ;"  Professor  Vignoles1  Lectures  ;  and  the  reports 
and  discussions  in  the  "  Civil  Engineer  and  Architect's  Journal ;" 
"  Journal  of  the  Franklin  Institute  ;"  "  American  Railroad  Journal,"  &c 

t  Ritchie  on  Railways,  p.  19. 


THEIR    HISTORY.  263 

Subsequently  these  wooden  rails  were  covered  with  plates 
of  iron  ;  but  the  introduction  of  rails  wholly  of  iron  seems 
not  to  have  taken  place  till  1767.*  A  projection,  or 
flange,  on  the  outer  side  of  the  rails,  kept  the  wheels  of 
carriages  upon  them.  They  were  then  called  "  Tram- 
roads."  The  objections  to  them  were  the  broad  surface 
of  the  plate,  which  collected  obstructions  upon  it,  and  the 
great  friction  of  the  wheels  against  the  side-flange. 

In  1789,  was  constructed  the  first  public  railway  in 
England,  at  Loughborough,  by  Mr.  William  Jessop,  and 
he  introduced  cast  iron  edge-rails,  and  wheels  with  the 
flanges  cast  upon  them  instead  of  on  the  rail.  "  Tram- 
roads"  were,  however,  still  in  use  in  1808.f 

In  1803,  malleable  iron  rails  were  first  tried,  but  not 
approved  cf.  In  1808,  they  were  introduced  into  some 
coal  works  in  Cumberland,  and  used  with  complete  suc- 
cess.! Since  that  time  they  have  become  almost  univer- 
sal, and  have  been  formed  into  a  great  variety  of  shapes, 
the  best  of  which  will  be  noticed  in  the  section  on  "  Con- 
struction." The  progress  from  the  use  of  horse  power  to 
locomotives  of  the  present  power  and  speed,  will  be  in- 
cluded in  the  examination  of  "  Motive  powers." 

In  our  condensed  sketch  of  the  extensive  subject  of 
Railroads,  divisions  and  subdivisions,  analogous  to  those 
of  the  previously  examined  topic  of  roads  in  general,  will 
be  employed,  and  thus  the  coincidences,  and  the  differ- 
ences, of  the  principles  appropriate  to  each,  will  be  made 
more  prominent  and  striking. 

The  following  is  an  outline  of  the  proposed  arrange 
ment : 


*  Hornblower's  Report  to  House  of  Commons  in  1811. 

•»  Ritchie,  p  22.  t  R.  Stevenson's  Report,  181ft. 


264  RAIL-ROADS 


RAILROADS  ouoi  ^  TO  BE. 

1.  AS  TO  THEIR  DIRECTION. 

2.  AS  TO  THEIR  GRADES. 

3.  AS  TO  THEIR  CROSS-SEOT1OR. 

II.  THEIR  LOCATION. 

III.  THEIR  CONSTRUCTION. 

1.  FORMING  THEIR  ROAD-BED, 

2.  THEIR  SUPERSTRUCTURE. 

IV.  THEIR  MOTIVE  POWERS. 

3-  HORSE  POWER. 

2.  STATIONARY  ENGINES. 

3.  LOCOMOTIVES. 

4.  ATMOSPHERIC  PRESSURE 


I.  WHAT  RAILROADS  OUGHT  TO  BE. 

To  determine  "  What  Railroads  ought  to  he,"  it  is  first 
necessary  to  ascertain  what  are  the  Resistances  to  motion 
upon  them  which  we  must  seek  to  overcome  or  diminish. 
The  nature  and  amount  of  these  resistances  upon  a 
straight  and  level  road  will  be  first  examined,  and  then 
their  increase  on  curves,*  and  on  ascents. f 

RESISTANCES  ON   A  STRAIGHT  AVD  LEVEL  ROAD. 

The  amount  of  these  resistances  has  been  usually  ta- 
ken al  8  Ibs.  to  a  gross  ton  of  2240  Ibs  ;  or  1  to  280  ;  i.  e. 
it  was  assumed  that  a  weight  of  eight  pounds  suspended 
from  a  cord  passing  over  a  pulley,  and  allowed  to  descend 
by  its  own  gravity,  (as  down  a  well)  would  draw,  on  a 

*  See  page  278.  t  See  IW  2?«- 


RESISTANCES.  265 

straight  and  level  railroad,  a  car  attached  to  the  other 
end  of  the  cord,  and  weighing  one  ton  ;  or  that  1  pound 
would  thus  draw  280  Ibs.  But  later  experiments  have 
shown  that  the  resistance  varies  with  the  velocity ;  that 
it  is  10  Ibs.  per  ton  at  a  speed  of  12  miles  per  hour,  and 
over  50  Ibs.  at  60  miles  per  hour.  The  most  satisfactory 
analysis  of  it,  is  given  by  the  following  empirical  formula, 
deduced  by  Mr.  Scott  Russell  (and  communicated  to  the 
British  association  in  1846)  from  experiments  on  five  dif- 
ferent railroads,  mostly  of  the  narrow  gauge. 

The  resistance  has  three  principal  elements  ;  Friction, 
Atmosphere,  and  Concussion. 

The  first  resistance  is  that  of  the  Friction  proper  of  the 
wheels  and  axles.  It  is  constant  at  all  velocities,  and 
amounts,  in  the  best-constructed  carriages,  to  6  Ibs.  per 
ton  weight  of  train.* 

The  second  resistance  is  that  of  the  Air.  It  is  con- 
sidered to  be  proportional  to  the  surface  of  the  front  of 
the  train,  and  to  the  square  of  the  velocity.  It  equals  the 
weight  of  a  column  of  air,  whose  base  is  the  frontage  of 
the  train,  and  whose  length  is  the  height  due  to  the  ve- 
locity. This  weight,  for  each  square  foot  of  frontage, 
and  for  a  velocity  of  one  mile  per  hour,  equals  0.0027  lb., 
or  <i^  lb.  For  the  usual  frontage  of  80  square  feet,  it 
is  therefore  one-fifth  of  a  pound  at  one  mile  per  hour. 

The  third,  or  residual  resistance,  is  probably  due  to 
the  unavoidable  Concussions,  oscillations,  flexures,  im- 
bedding of  wheels  in  rail,  friction  of  air  against  sides,  &c. 
It  may  be  hereafter  decomposed  into  various  elements, 
but  is  now  taken  as  proportional  to  the  weight  of  the  train 
and  the  velocity,  and  as  being  equal  to  J-  lb.  for  each  ton 
of  train,  at  one  mile  per  hour. 

*  The  tons  here  used  are  all  gross  tons  of  -J240  Ibg. 


•<>66  RAIL-ROADS. 

We  are  now  prepared  to  find  the  resistance  (in  Ibs.)  of 
a  straight  and  level  railroad  to  the  motion  of  a  train  ot  ' 
cars,  whose  weight  (in  tons),  velocity  (in  miles  per  hour), 
and  frontage  (in  square  feet),  are  given,  by  the  following 

RULE. 

1.  Multiply  the  weight  by  6,  —  for  friction. 

2.  Multiply  the  weight  by  the  velocity,  and  divide  by 
3,  —  for  concussion. 

3.  Square  the  velocity,  and  multiply  this  square  by  the 
frontage,  and  divide  this  product  by  400,  —  for  the   at- 
mosphere. 

4.  Add  these  three  results,  and  the  sum  is  the  total 
resistance.     Divide  this  by  the  weight,  and  the  quotient 
is  the  resistance,  per  ton. 

Example  1.  A  freight  train  of  100  tons  is  to  be  drawn  12 
miles  per  hour.  Its  frontage  is  80  square  feet  What  is  the 
resistance  to  be  overcome  by  the  motive  force  ? 

Friction         =      100  X    6      =600  Ibs. 

100  X  12 

Concussion    =      -  -  -      =     400    " 
o 

12  X  12  X  80 

Atmosphere  =  -  —  -  =  _29    « 

Total  resistance  =  1029  Ibs. 

1029 
Resistance  per  ton  =  "TTJTT  —  10*  lbs- 

Example  2.  A  passenger  train  of  50  tons  is  to  be  drawn  35 
miles  per  hour.  Its  frontage  is  80  square  feet.  Required  its 
resistance. 

Friction         =     50  X    6       =    300  Ibs. 

50  X  35 
Concussion    =      -  -  -       =    583    " 

O 

35  X  35  X  80 
Atmosphere  =s  -  —  -  =    245    " 


Total  resistance  =1128  Ibs. 

12 
rr 


1128 
Resistance  per  ton  =  -rr-  =  22|  Ibs 


RESISTANCES. 


267 


Example  3.  A  train  of  25  tons,  at  60  miles  per  hour,  would 
meet  a  resistance  (by  both  theory  and  experiment)  of  55  Ibs.  per 
ton.  This  rapid  increase  of  resistance  with  velocity,  is  very 
striking,  though  it  has  been  disputed  by  some  experimenters. 

The  above  formula  has  been  tested  by  Mr.  Scott  Rus- 
se!',  and  Mr.  Wyndham  Harding,  chiefly  for  passenger 
trains  of  from  20  to  64  tons,  and  at  speeds  from  30  to  60 
miles  per  hour.  At  lower  velocities,  its  results  some- 
what exceed  those  of  the  experiments.  When  the  rail- 
road or  carriages  are  in  bad  repair,  or  side-winds  prevail, 
the  resistances  will  be  greater  than  are  here  given.  For 
head-winds,  the  velocity  of  the  wind  should  be  added  to 
that  of  the  train. 

The  following  Table  shows  the  Resistances  to  Trains 
of  different  weights,  and  at  different  velocities,  as  given 
both  by  actual  experiments  and  by  the  above  formula : 
the  frontage  being  60  square  feet. 


Velocity. 

w  .  ,  t  [Resistance 
VV  eight.  |byExper 

S^Velocity. 

Weight. 

Resistance 
by  Exper. 

Resist,  by 
Formula. 

mi.  per  ttr. 

14 

ton*. 
9 

lit.  per  ion. 

12.6 

los.  per  ton. 

13.9 

mi.  per  hr. 

34 

ton*. 

301 

lit.  per  ton. 

25.0 

Ita.  per  ton. 

23.1 

16 

201 

8.5 

13.2 

34 

18" 

23.4 

27.2 

19 

40| 

8.5 

12.9 

35 

2U 

22.5 

26.1 

21 

18 

12.6 

16.7 

39 

24 

30.0 

31.0 

25 

40£ 

12.6 

16.6 

47 

31? 

33.7 

33.1 

27 

40£ 

12.6 

17.7 

50 

30 

32.9 

35.3 

31 

151 

23.4 

25.4 

53 

25 

41.7 

42.1 

32 

141 

22.5 

27.2 

61 

211 

52.6 

54.8 

When  the  motive  power  is  a  Locomotive  Engine,  Us 
own  resistance  must  also  be  taken  into  account.  The 
friction  on  its  machinery,  or  working  parts,  may  be  taken 
at  7  Ibs.  per  ton  of  its  weight ;  and  its  friction  considered 
as  a  carriage  at  8  Ibs.  per  ton.  To  this  should  be  added. 


268  RAIL-ROADS. 

according  to  Pambour,  1  Ib.  for  each  ton  of  the  load  drawn 
by  it.  Its  atmospheric  resistance  is  already  taken  into 
account,  since,  if  again  calculated  and  attributed  to  the 
engine,  it  should  be  deducted  from  the  train  of  cars,  which 
the  engine  in  front  of  them  shields  from  it. 

The  usual  mode  of  recording  the  resistance  as  so  many 
Ibs.  "  per  ton,"  does  not  give  a  satisfactory  standard  of 
comparison  ;  one  of  the  resistances  (that  of  the  atmo- 
sphere) being  independent  of  the  weight  of  the  train.  An 
increase  of  this  weight  (which  is  the  divisor  of  the  whole) 
would  therefore  lessen  the  resistance  per  ton,  while  it  in- 
creased the  total  resistance. 

On  the  other  hand,  this  atmospheric  resistance  no  doubt 
varies  somewhat  with  the  length  of  the  train,  and  the  con- 
sequent increased  friction  of  the  air  against  the  sides  of 
the  carriages.  Dr.  Lardner  (in  his  report  of  1841  to  the 
British  Association)  considers  "  the  resistance  due  to  the 
air  to  proceed  from  the  effect  due  to  the  entire  volume  of 
the  train,  and  not  to  depend  in  any  sensible  degree  on  the 
form  of  the  foremost  car."  Sharp  fronts  did  not  diminish 
it,  nor  did  an  increased  frontage  (as  formed  by  boards 
projecting  on  each  side)  much  increase  it.  Barlow,  in  a 
paper  read  before  the  Royal  Society  in  1836,  considers 
the  resistance  of  the  air  to  increase  in  a  ratio,  not  as  the 
square,  but,  not  much  higher  than  the  simple  velocity. 

A  new  formula,  which  assumes  this  resistance  to  be 
directly  proportional  to  the  bulk  of  the.  train,  and  which 
also  more  minutely  analyzes  the  resistances  of  the  engine, 
has  been  deduced  by  Mr.  D.  Goochf  from  experiments 
made  in  1848  on  a  "  broad  gauge"  road.  His  results 
have  been  much  disputed.  The  following  is  an  analysis 
of  them :— 


RESISTANCES.  260 

For  the  CARS,  the  Fractional  resistance  is  taken  a*  6  Ibs.  oer 
ton,  as  before. 

The  Atmospheric  resistance  is  assumed  as  equal  to  the  sqnaro 
of  the  velocity,  multiplied  by  the  bulk  of  the  train  in  cubic  feet, 
and  that  product  by  -n^mi-  Each  ton  weight  of  the  train  is 
supposed  to  correspond  to  180  cubic  feet.  The  atmospheric  re- 
sistance obtained  by  this  formula  would  equal  that  given  by 
Russell,  in  the  case  of  a  load  of  55£  tons.  For  a  greater  load, 
this  formula  makes  this  resistance  proportionally  greater  than 
Russell's,  and  for  a  less  load  proportionally  less. 

The  residual  or  oscillatory  resistance  is  taken  at  only  -^  the 
product  of  the  velocity  by  the  weight,  instead  of  5,  as  in  the 
former  formula.  Mr.  Gooch  considers  this  "  oscillatory"  re- 
sistance to  be  mainly  the  increased  friction  of  the  axle  bearing 
upon  its  collars,  in  consequence  of  the  transverse  vibrations  at 
high  velocities,  while  Mr.  Russell  makes  it  include  all  the  re- 
sistances remaining,  after  "  friction"  and  "  atmosphere"  are  de- 
ducted from  the  total  amount. 

Example  4.  Let  weight  of  train  =  100  tons ;  velocity  =  50 
miles  per  hour ;  required  the  resistance  to  the  motion  of  the 
cars. 

Friction        =  100  x  6        -        -        -        -       =600  Ibs. 
Oscillation    =  5A^°_°       .        .        .        .       =    333   « 

Atmosphere  =  50  X  50  X  100  X  180  X  1003oog  =    900   " 
Total  resistance  of  cars     =  1833  Ibs. 

For  the  ENGINE  and  tender,  the  resistance  is  separated  into 
two  parts.  That  caused  by  the  friction  of  axles  and  machinery, 
is  (in  pounds  per  ton  of  their  weight)  equal  to  5,  plus  one  half 
the  velocity  in  miles  per  hour.  That  due  to  atmosphere  and  load 
equals  y^Vsr  °f  tne  square  of  the  velocity  multiplied  by  the 
weight  of  the  train.  These  resistances  would  of  course  be  dif 
ferent  for  each  different  engine. 


270  RAIL-ROADS.     ' 

Example  5.  With  -weight  of  train  —  1 00  tons ;  velocity  —  50  miles; 
and  Engine  and  tender  =  50  tons,  required  resistance  of  the  Engine 
and  tender. 

6.  +  i  X  50  =  30  Ibs.  per  ton  of  their  weight. 
TOJ^.  X  50  X  50  X  100  —  H>       " 

Or,  the  total  resistance  of  Engine  and  tender  —  40  X  50 «—  2000  lb* 
Total  resistance  of  Train  and  Engine  =  1833  +  2000  —  3833  Ibs., 

ori^;^-- 25.5  Ibs.  per  ton. 

The  discrepancies  in  the  results  obtained  by  various 
experimenters  and  theorizers,  show  the  great  deficiencies 
which  exist  in  the  data  of  the  experiments  and  in  the  ap- 
plication of  the  theoretical  principles  involved. 

Assuming  for  the  present  Mr.  Scott  Russell's  formula 
to  be  approximately  correct,  we  are  next  to  examine  the 
increased  resistances  which  occur  on  CURVES,  and  on 
ASCENTS.  This  will  be  done  under  the  heads  of  "  What 
Railroads  ought  to  be,"  as  to  their  Directions,  and  as  tc 
their  Grades. 

1.  WHAT  RAILROADS  OUGHT  TO  BE  AS  TO  THEIR  DIRECTION. 

Straightness  of  direction  is  much  more  important  on 
railroads  than  on  common  roads,  for  two  reasons ,  the 
economy  of  Straightness,  and  the  resistances  and  dangers 
of  curves. 

ECONOMY    OF    STRAIGHTNESS. 

From  the  great  cost  of  the  superstructure  of  a  railroad, 
and  the  continually  increasing  expense  of  keeping  it  in  re- 
pair, it  is  highly  desirable  that  it  should  be  as  straight,  and 
consequently  as  short,  as  possible. 

As  the  earthwork  of  a  railroad  costs  almost  nothing  for 
repairs,  while  those  of  its  perishable  superstructure  arc 
very  great,  and  proportioned  to  its  length,  as  is  also  the 
cost,  in  fuel,  wages,  and  wear  and  tear  of  the  engines, 
of  running  the  road,  it  will  often  be  advantageous  to 


ECONOMY  OF    STRAIGHTNESS.  271 

make  large  expenditures  for  the  former  element  of  cost, 
in  order  to  lessen  the  length  of  the  road,  and  consequently 
the  annual  expenditures  for  the  latter.* 

Suppose  the  total  cost  of  a  railroad  to  be  $30,000  per 
mile,  the  interest  of  which  is  $1800;  the  annual  repairs 
of  the  superstructure  $1000  per  mile  ;  and  the  expenses 
of  engines  also  $1000  per  mile.  The  total  annual  ex- 
pense will  then  be  $3800,  which  is  the  interest  of  $63,000, 
which  sum  might  prqfitably  be  expended  to  shorten  the 
road  one  mile,  or  $12  to  shorten  it  one  foot  of  length.  If 
this  single  foot  gained  was  the  only  result  of  a  day's  labor 
of  a  locating  party,  it  would  be  a  satisfactory  equivalent 
for  the  expenses  of  such  a  day's  work. 

On  these  grounds,  a  short  route,  which  has  the  faults 
of  steep  grades  and  curves  of  small  radius,  may  profitably 
receive  an  outlay  of  capital  upon  it,  for  the  purpose  of 
lessening  these  defects,  equivalent  to  the  cost  of  the  dif- 
ference of  distance  between  it  and  a  longer  line,  which 
has  better  grades  and  curves. 

From  these  considerations  it  is  also  seen  that  a  line 
ought  not  to  diverge  from  the  direct  course  between  its 
extremities,  and  thus  increase  its  distance,  for  the  sake  of 
the  trade  of  a  small  town,  for  whose  benefit  the  time  and 
fare  of  all  the  passengers  and  freight  on  the  whole  line 
would  thus  be  taxed.  It  would  be  preferable  to  make  a 
branch  track  to  the  town. 

EVILS    OF    CURVES. 

Curves  are  necessary  evils  on  most  routes,  enabling 
them  to  pass  around  obstacles,  such  as  projecting  hills, 
deep  hollows,  houses  too  valuable  to  be  removed,  &c. 

*  See  Amer.  Railroad  Journal,  August,  1839,  foi  an  able  development 
of  this  position  by  W.  B.  Casey,  C  E. 
18 


272  RAIL-ROADS. 

The  greatest  economy  in  curving  is  found  when  the  line 
is  located  in  a  narrow  and  sinuous  valley,  with  rocky 
banks,  whose  windings  can  be  cheaply  followed  by  suita 
bly  adjusted  curves.  When  the  line  crosses  a  series  of 
ridges  transversely,  and  nearly  at  right  angles  to  their 
general  direction,  there  would  be  little  economy  in  lateral 
deviation  and  curvature. 

The  evils  of  curves  are  the  resistances  which  they  offer 
to  the  motion  of  cars,  and  the  dangers  to  which  they  ex- 
pose them. 

The  following  are  the  four  principal  causes  of  the  resis- 
tances on  curves :* 

1.  The  obliquity  of  the  direction  of  the  moving  power; 
i.  e,  the  angle  which  the  line  of  traction,  drawn  from  the 
engine  to  each  car,  makes  with  the  tangent  to  the  curve 
at  the  middle  of  each  car,    in  the  direction  of  which  the 
cars  tend  to  move. 

2.  The  pressure  and  consequent  friction  of  the  flanges 
of  the  wheels  against  the  outer  rail,  due  to  the  centrifugal 
force. 

This  is  partially  obviated  by  elevating  the  outer  rail,  as 
will  be  hereafter  explained. 

3.  The  pressure  and  consequent  friction  of  the  flanges, 
due  lo  the  parallelism  of  the  axles  ;  for  the  directions  of  the 
tangents  at  the  points  of  contact  of  each  pair  of  wheels 
are  different,  and  therefore  if  one  pair  of  wheels  be  per- 
pendicular to  its  corresponding  tangent,  the  other  pair 
will  be  oblique  to  its  tangent. 

This  resistance  is  panly  remedied  by  allowing  a  "  play" 
of  an  inch  or  less  between  the  wheels  and  the  rails.  It 
diminishes  as  the  axles  are  placed  nearer  to  each  other . 

»  Re  x>rt  of  E.  F.  Johnson,  C.  E.,  1848 


RESISTANCES    OF    CURVES.  273 

and  is  therefore  much  lessened  by  supporting  the  cars 
on  two  trucks,  eacli  resting  on  four  wheels,  the  two  axles 
of  which  are  very  near  to  each  other. 

4.  The  fastening  of  each  pair  of  wheels  to  the  same 
axle,  with  which  they  turn.*  The  wheel  on  the  outer 
side  of  a  curve  must  revolve  farther,  and  therefore  faster, 
than  the  inner  one,  which  must  slide  (if  both  are  of  the 
same  diameter)  by  an  amount  equal  to  the  difference 
between  the  lengths  of  the  inner  and  outer  rails  of  the 
curve. 

To  lessen  this  resistance,  the  wheels  are  made  conical, 
with  their  inner  diameters  greater  than  the  outer,  so  that 
on  curves,  the  outer  wheels  run  on  their  greater  diameter 
and  the  inner  ones  on  the  less.  This  cone  may  be  so 
adjusted,  that  the  wheel  can  run  in  a  circle  of  595  feet 
diameter  without  the  flanges  touching  the  rail.  It  was 
at  first  1  in  7,  but  has  of  late  been  reduced  to  ^o  and  ^5-. 

Without  these  arrangements,  the  resistance  of  a  curve 
of  even  a  mile  in  radius,  at  a  speed  of  25  miles  per  hour, 
would  equal  that  of  an  ascending  grade  of  9|-  feel  per 
mile  ;  and  one  of  700  feet  radius,  a  grade  of  77  feet,  <&c. 

The  actual  resistance  has  been  very  imperfectly  ascer 
tained. 

Grave  objections  have  been  urged  by  eminent  engi- 
neers against  "coning"  the  wheels.  One  is,  that  if  the 
rail  is  canted  so  as  to  fit  the  coning,  on  the  straight  line 
portions  of  the  road  there  will  be  a  constant  grinding 
action,  owing  to  the  dragging  of  the  outer  and  smaller 
portions  of  the  wheels.  It  is  also  stated  that  much  of 
the  concussions  of  the  flange  of  the  wheel  against  the 
rail  is  due  to  the  coning,  and  that  where  cylindrical 


*  If  they  turned  on  the  axle,  as  in  ordinary  carriages,  they  \vcr.ld 
net.  have  sufficient  steadiness  to  run  truly  at  high  velocities. — LBCOINT, 
p  134. 


374  RAIL-ROADS. 

surfaces  have  been  used  for  the  wheels  (instead  of  the 
conical  ones,  as  is  usual),  the  trains  hare  ran  much 
steadier. 

The  actual  resistance  on  curves  has  been  very  imper- 
fectly ascertained.  See  note  on  page  454. 

The  amount  of  mechanical  power  absorbed  in  passing 
around  a  curve  is  altogether  independent  of  the  radius  of 
the  curve,  and  depends  only  on  the  amount  of  the  entire 
angular  change  in  the  direction  of  the  line.  When  the 
curve  has  been  run  by  "  Angles  of  deflection,"  its  length 
in  chains,  multiplied  by  its  angle  of  deflection,  equals  the 
entire  angular  change.  Thus,  a  curve  of  1°,  30  chains 
long,  offers  the  same  resistance  as  one  of  3°,  10  chains 
long.*  Sharp  curves  are  therefore  not  objectionable  on 
the  score  of  loss  of  power,  though  highly  so  from  their 
wear  and  tear  of  engines  and  cars,  displacement  of  rails, 
danger,  &c. 

The  danger  of. running  off  the  track  is  much  increased 
by  curves,  even  of  large  radius,  especially  at  high  ve- 
locities. The  momentum  of  the  cars  impels  them  onward 
in  a  straight  line,  and  they  are  kept  within  the  rails  only 
by  the  flanges  of  the  wheels  and  the  firmness  of  the 
outer  rail,  the  resistance  of  which  gradually  makes  them 
follow  the  curvature  of  the  road.  If  the  momentum 
should  exceed  the  resisting  force,  the  cars  must  obey  the 
former  and  leave  the  track.  Curves  at  the  foot  of  incli- 
nations are  therefore  especially  objectionable,  since  the 
cars  will  come  upon  them  with  excessive  velocity.  The 
rocking  and  twisting  motion  thus  given  to  the  cars  indi- 
cates the  dangerous  tendency  which  they  thus  acquire. 

*  The  angle  of  deflection  of  any  curve  may  be  found  by  dividing  5730 
by  its  radius  in  feet. 


CURVES.  275 

When  sharp  curves  are  unavoidable,  they  should,  if 
possible,  be  located  near  stopping-places.  They  should 
not  be  placed  on  a  steep  slope,  on  account  of  the  double 
resistance  which  would  then  be  caused  to  trains  ascend- 
ing, and  the  increased  danger  of  running  off  to  trains  rap 
idly  descending.  But  if  such  location  on  a  long  slope  be 
unavoidable,  the  grade  should  be  flattened  along  the  curve, 
and  the  difference  applied  to  the  straight  portions.  Curves 
should  not  be  in  deep  cutting,  where  the  impossibility  of 
seeing  far  ahead  might  cause  collisions,  but  on  the  parts 
in  embankment,  or  on  the  surface. 

The  increased  velocities  of  the  more  recent  railroads 
have  greatly  lessened  the  permissible  smallness  of  the 
radii  of  curves.  For  the  usual  speeds  employed  on  the 
English  railways,  it  is  recommended,  that  the  minimum 
radius  should  be  one  mile.  On  the  Baltimore  and  Ohio 
railroad,  however,  one  of  the  earliest  in  the  United  States, 
there  are  several  curves  of  400  feet  radius,  (14{°)  ana  one 
of  318  feet,  (18°)  over  which  locomotives  pass  without 
difficulty  at  a  speed  of  15  miles  per  hour. 

The  minimum  in  France,  allowed  by  "  L' Administra- 
tion des  Fonts  et  Chaussees"  is  2700  feet ;  or  about  2°. 

The  minimum  curve  upon  the  Hudson  River  railroad 
has  a  radius  of  2062  feet=2f°. 

By  the  Parliamentary  "  Standing  Orders"  of  1846,  a 
Railroad  Company  cannot  diminish  the  radius  of  any 
curve  to  less  than  half  a  mile  (2640  feet)  without  the 
special  permission  of  Parliament. 


276  EFFECTS    OF    GRADES. 


2.   WHAT  RAILROADS  OtTGHT  TO  BE  AS  TO  THEIR  GRADE& 

The  question  of  the  steepest  grade  admissible  on  a 
railroad  is  not  one  of  practicability,  as  is  often  supposed, 
but  only  one  of  comparative  economy.  Locomotive  en- 
gines can  be  made  to  ascend  grades  of  almost  unlimited 
steepness,  by  a  proportionate  increase  of  their  power  and 
adhesion,  but  their  ascent  becomes  less  and  less  useful  in 
proportion  as  the  grades  become  more  and  more  steep. 
On  an  ascent  of  19  feet  to  the  mile,  an  engine  can  draw 
only  about  one-half  its  load  on  a  level ;  at  38  feet  to  the 
mile,  only  one-third,  and  so  on,  (adopting  the  usual, 
though  insufficient,  ratio  of  8  Ibs.  to  the  ton,  or  1  to  280, 
as  the  resistance  on  a  level)  since,  on  this  supposition, 
if  the  railroad  rises  1  foot  in  280,  an  additional  force  of 
8  Ibs.  will  be  required  to  draw  one  ton  up  this  ascent, 
(see  page  32)  and  therefore  double  the  former  force  will  be 
needed  to  draw  the  former  load.  Only  half  the  load, 
therefore,  could  be  drawn  by  the  same  force  ;  or  that 
amount  of  power  which  could  draw  a  load  a  mile  on  a 
level,  would  be  exhausted  in  drawing  it  half  a  mile  up 
this  ascent.* 

*  The  precise  ratio  between  the  total  resistance  on  a  level  road,  and 
that  on  any  ascent,  and  therefore  between  the  comparative  loads  which 
can  be  carried  on  each,  may  be  found  by  the  proportion  which  will  now 
bo  investigated. 

The  loads  on  a  level,  and  on  an  ascent,  are  in  the  inverse  ratio  of  the 
resistance  thereon  :  i.  e. 

The  load  on  the  level  is  to  the  load  up  the  ascent,  as  the  total  resist- 
ance on  the  ascent  in  to  the  resistance  on  the  level. 

The  resistance  on  the  ascent  is  compounded  of  that  of  friction,  &c.  ou 
the  level,  and  that  of  gravity,  which  is  such  a  part  of  the  whole  ioadj  as 
the  height  of  the  ascent  is  of  its  length,  as  shown  on  page  32. 


RESISTANCES    ON    ASCENTS.  271 

Adopting  the  more  correct  ratio  of  10£  Ibs.  per  ton,  or 
1  to  218,  as  the  resistance  at  the  asus.1  freight  speed  of 
12  miles  per  hour,  (see  page  266)  it  would  require  an 
ascent  of  24  feet  per  mile  to  double  it,  48  feet  to  triple  it, 
and  so  on.  When  the  resistance  is  increased  to  20  Ibs.  per 
ton,  or  1  to  112.  (as  in  the  case  at  high  velocities)  an  as- 
cent of  47  feet  per  mile  is  required  to  double  it  ;  and  a 
resistance  of  30  Ibs.  per  ton  corresponds  to  an  ascent  ot 
70  feet. 

These  results  show  that  heavy  grades  are  proportion- 
ally less  injurious  on  a  road  where  great  speed  is  em- 
ployed, with  correspondingly  great  resistances,  though  the 
absolute  loss  of  power  caused  by  them  remains  the  same. 
The  late  discovery,  that  the  resistances  at  even  slow  rates 
of  travel  are  greater  than  had  been  supposed,  lessens 
greatly  the  objections  to  heavy  grades,  and  shows  them 
to  be  relatively  much  less  injurious  than  had  been  imag- 
ined, seeing  that  so  much  greater  an  ascent  is  required  to 
double  the  resistance.  Besides,  a  small  diminution  in  the 

Let  then  f=  Resistance  (in  Ibs.  per  toil)  on  a  level. 

A  =  Ascent  in  feet  per  mile  ;  and—--  =  Inclination. 

—  —  -  X  2240=-  —  —  =  Resistance  per  ton  of  Gravity. 
5^oO  33 

14A 
/+-—-=  Total  resistance  on  the  inclination. 

39 
The  above  proportion  then  becomes, 

Load  on  level  :  Load  up  ascent  :  :  /  +  -QO~  :  /•  Whence, 

f  Load  on  level 

Load  up  ascent  =  Load  on  level  X  -  "   A1    =  -  j  —  5- 
14A  14A 

~  +     ~ 


When  the  motive  power  is  a  Locomotive  Engine,  as  is  usual,  its  weight 
must  be  included  in  the  "  Load  on  level,"  used  in  the  calculation,  and 
finally  subtracted  from  the  resulting  "  Load  up  ascent." 

Example.  —  Let  the  weight  of  the  cars  drawn  on  a  level,  at  12  miles 
per  hour,  be  447  tons  ;  the  engine  23,  and  the  tender  14  tons  :  required 


278  RAIL-ROADS. 

velocity  of  the  train  would  compensate  for  the  increased 
resistance  of  quite  a  steep  grade. 

The  cost  of  draught  on  a  railroad  is  nearly  as  the  power 
employed,  so  that  it  will  cost  nearly  twice  as  much  to 
carry  a  load  on  a  railroad  with  an  ascending  grade  of  24 
feet  to  the  mile,  as  to  carry  it  on  a  level  route.  This 
consideration  will  therefore  justify  large  expenditures 
upon  the  excavations,  embankments,  &c.,  of  a  railroad, 
with  a  view  of  reducing  its  grades.  The  propriety  of 
such  expenditures  is  to  be  determined  by  comparing  the 
annual  interest  of  the  amount  with  the  annual  saving  of 
power  ever  after,  in  drawing  the  expected  loads  over  the 
flattened  road. 

But,  on  the  other  hand,  this  principle  may  be  carried  to 
excess.  These  great  expenses  for  graduation  should  be 
incurred  only  when  maximum  loads  are  to  be  constantly 
carried  at  high  speeds,  as  on  important  leading  lines  of 
great  traffic.  Much  steeper  grades,  than  would  be  other- 
wise allowable,  may  be  adopted  on  roads  on  which  maxi- 
mum loads  are  not  often  carried,  and  on  which  the  trains  are 
required  for  public  convenience  to  go  often,  and  will 
therefore  generally  go  light.  The  engine  may  be  able  to 
draw  400  tons  on  a  level,  and.may  seldom  have  more 
than  100  to  draw.  In  such  cases  the  true  economy  is, 

tho  load  which  the  same  power  can  draw  up  an  ascent  of  10  feet  per 
mile. 

Here/=  10J,  and  h  =  10.     By  the  above  formula, 

(447  +  20+14)  481 

Load  up  ascent  =  —  =  =  341.1 


33X10i 

341.1—  (20  +  14)  =  307,1  =  The  load  up  the  ascent. 
For  the  method  of  calculating  the  tractive  power  of  locomotives,  see 
page  325. 


EFFECTS    OF    GRADES.  279 

not  to  go  to  great  expense  in  order  to  reduce  the  grades 
below  such  a  degree  of  steepness  as  would  permit  the 
engines  to  draw  up  their  usual  small  loads  ;  nor  to  attempt 
to  make  a  very  level  road,  on  which  the  engines  could  do 
a  great  deal,  but  would  have  very  little  to  do.  The 
same  reasoning  applies  to  railroads  between  places  fur 
nishing  but  a  moderate  amount  of  travel,  such  as  the 
thinly  settled  parts  of  this  country.  Should  the  travel 
subsequently  greatly  increase,  in  an  unanticipated  degree, 
more  frequent  light  trains  could  be  sent.  The  enormous 
expenditures  sometimes  made  in  such  situations  to  make 
a  perfect  road,  have  been  too  great  for  the  scanty  travel 
to  pay  interest  upon,  and  have  discouraged  the  proper 
construction  of  such  as  would  have  been  really  profitable. 

A  great  reduction  of  the  first  cost  of  a  railroad  may  often 
be  made,  without  much  increasing  its  •  subsequent  ex- 
penses ;  inasmuch  as  the  capital  expended  in  the  gradua- 
tion of  a  road  has  averaged,  in  England,  fifteen  times  the 
cost  of  the  locomotive  power ,  and  as  the  daily  cost  of 
transit,  due  to  this  last,  is  also  very  small.  Locomotive  pow- 
er forms  only  about  one-third  of  the  whole  working  expen- 
ses of  a  road ;  and  only  a  part  of  this,  say  one-half,  is  likely 
to  be  affected  by  the  grades  ;  so  that  there  is  only  one- 
sixth  of  the  whole  working  expenses,  which  can  be  saved 
by  making  a  road  theoretically  perfect  in  grades  ;  a  small 
consideration  for  the  interest  of  the  extra  capital,  unless 
the  traffic  is  likely  to  be  continued,  regular,  and  very 
heavy. 

In  brief,  first  determine  precisely  what  is  wanted.  If 
the  best  possible  road  would  be  justified  by  the  import- 
ance of  the  traffic,  make  it  as  perfect  (i.  e.  as  straight, 
level,  and  unyielding)  as  possible,  so  that  it  can  accom- 
plish the  greatest  arnoun-  of  labor  in  the  least  time  and 


280  RAIL-ROADS. 

with  the  smallest  expenditure  of  power.  If  a  cheap 
though  inferior  road  will  accommodate  the  traffic  expect 
ed,  let  such  a  one  be  made. 

In  comparing  two  roads  between  the  same  points,  one 
of  which  is  level  and  the  other  has  a  summit,  reached  by 
an  ascending  grade,  succeeded  by  a  descending  one,  it 
must  not  be  overlooked  that  there  is  a  certain  degree  of 
compensating  power  in  the  descent.  As  to  how  much  of 
the  power  lost  in  the  ascent,  is  gained  by  the  assistance 
of  gravity  in  the  descent,  there  is  great  difference  of 
opinion.  It  was  formerly  supposed  that  on  descents 
steeper  than  the  angle  of  repose,  1  in  280,  or  19  feet  to 
the  mile,  the  cars  would  be  accelerated  by  the  force  of 
gravity,  (which  is  just  balanced  by  friction  at  that  incli- 
nation) and  that  the  brake  would  then  need  to  be  ap- 
plied, so  that  beyond  that  limit  no  more  assistance  could 
be  derived  from  gravity.  But  it  has  been  found  by  recent 
experiments  that  the  resistance  of  the  air  to  the  motion  of 
cars  is  far  greater,  and  increases  with  the  speed  much 
faster,  than  had  been  imagined.  This  resistance,  there- 
fore, opposes  the  accelerating  tendency  of  gravity  with  a 
force  increasing  with  the  velocity,  so  that  trains  of  cars 
may  safely  descend  inclinations  of  60  feet  to  the  mile.  On 
planes  of  53  feet  to  the  mile,  trains  have  commenced 
the  descent  at  a  speed  of  40  miles  per  hour,  but  instead 
of  this  velocity  being  increased,  it  was  reduced  to  30 
miles  per  hour.  Railroads  may  therefore  be  laid  out 
with  grades  of  nearly  60  feet  to  the  mile,  with  little  or  no 
loss  of  power  in  the  descent ;  and  there  is  little  practical 
Joss  of  power  in  the  ascent,  if  the  loads  are  such  as  do 
not  task  the  engines  to  their  full  power  on  the  level  por 
lions  of  the  road.  In  England  it  has  been  found  that 
cheap  lines  with  steep  grades  have  not  cost  much  more  to 


UNDULATING    RAIL-ROADS.  281 

work  them  than  some  which  had  cost  two.  to  three  hun- 
dred thousand  dollars  per  mile.  We  may  therefore  con- 
clude that  Navier's  maxim,  that  "  The  amount  of  power 
required  to  effect  the  transit  of  a  line  of  railroad,  depends 
entirely  on  the  length  of  the  line  and  the  difference  of 
level  of  its  two  extremities,"  is  true,  if  none  of  the  incli- 
nations upon  it  exceeds  60  feet  to  the  mile,  and  if  the 
engine  is  not  obliged  to  carry  its  maximum  load  on  a 
level. 

This  principle  of  compensation  on  descents  was  carried 
to  such  excess  a  few  years  ago,  that  it  was  sanguinely 
recommended  to  make  all  railroads  undulating,  carefully 
avoiding  all  levels,  and  establishing  a  continual  succession 
of  ascents  and  descents.  It  was  argued  that  the  momen- 
tum which  the  cars  acquired  in  descending  one  slope, 
would  carry  them  up  the  next,  just  as  a  pendulum  swings 
as  far  to  the  one  side  as  to  the  other ;  and  that  having 
received  an  impelling  force  at  one  end  of  the  road,  they 
would  reach  the  other  end,  down  one  of  these  slopes  and 
up  the  next  in  turn,  by  the  assistance  of  gravity  alone. 
Volumes  have  been  written  in  attack  and  defence  of 
this  theory  ;  but  the  .most  fatal  objection  to  it,  even  sup- 
posing the  undulations  all  properly  arranged,  is,  that  the 
velocity  which  a  train  must  have  acquired  when  it  had 
reached  the  foot  of  one  slope,  to  be  sufficient  to  carry  it 
up  the  next,  would  be  too  great  for  safety,  and  that  the 
irregularities  of  speed  would  be  destructive  to  the  cars 
end  to  the  road. 


282  RAIL-ROADS. 

3.    WHAT    RAILROADS    OUGHT    TO    BE    AS    TO    THEIR    CROSS. 
SECTION. 

The  width  of  a  railroad  is  the  first  element  of  its  cross 
section  to  be  considered,  and  it  depends  upon  the  width 
between  the  inner  sides  of  the  rails,  which  is  called  its 
"  Gauge." 

THE  BROAD  AND  NARROW  GAUGE  QUESTION. 

The  customary  gauge  is  4  feet  8^  inches  ;  varying  from 
4»8  to  4»9,  according  to  the  space  deemed  necessary  for 
the  play  of  the  flanges  of  the  wheels.  This  is  called 
the  "  narrow  gauge."  The  "  broad  gauge,"  first  intro- 
duced by  Mr.  Brunei,  on  the  Great  Western  Railway  in 
England,  is  7  feet.  Between  these  two  gauges  is  still 
going  on  the  fiercest  contest  of  the  many  which  nave 
arisen  on  the  various  doubtful,  points  in  the  construction 
of  railroads. 

The  original  railroads  were  made  of  the  same  width  as 
the  tram-roads,  on  which  ran  common  wagons.  This 
width  happened  to  be  4  feet  8£  inches.  The  new  rail- 
roads adopted  the  same  width,  for  the  convenience  of 
using  upon  them  the  same  cars,  and  thus  this  width  be- 
came almost  universal.  Our  American  roads,  using  at 
first  English  engines,  were  necessarily  formed  with  an 
identical  gauge.  Other  gauges  have  also  been  employed. 
Four  feet  10  inches  is  the  New  Jersey  and  Ohio  gauge. 
Five  feet  is  the  gauge  of  Virginia,  East  Tennessee,  and 
the  north  of  Georgia.  Five  feet  6  inches  is  the  gauge 
in  Maine,  (Atlantic  and  St.  Lawrence  Road)  in  Can- 
ada, (by  general  law)  and  in  Missouri,  (by  law  of 
1835).  Six  feet  is  the  gauge  <  f  the  Erie  Railroad,  and 
of  its  connecting  roads. 


THEIR  GAUGE. 


283 


ADVANTAGES  OF  THE  BROAD  GAUGE. 

The  track  being  wider,  the  cars  have  a  broader  base ; 
so  that  if  the  frost,  or  any  other  cause,  raises  or  lowers 
one  side  of  the  road  a  certain  amount,  say  one  inch,  it 
will  cause  an  angular  inclination  of  only  1  in  84  on  the 
wide  track,  but  1  in  56^  on  the  narrow  one. 

The  breadth  of  base  being  greater,  the  centre  of  gravity, 
with  equal  loads,  is  lower ;  so  that  there  is  less  danger  of 
the  cars  running  off  the  track.  They  have  also  less  lat- 
eral motion  and  greater  steadiness,  and  thus  add  much  to 
the  comfort  of  the  traveller.  This  steadiness  may  also  be 
increased  by  placing  the  wheels  outside  of  the  cars. 

The  broader  base  permits  the  wheels  of  the  cars  to  be 
proportionally  increased  in  size,  and  thus  is  obtained  great-, 
er  leverage  for  overcoming  the  friction  at  the  axles. 

Instead  of  letting  the  cars  remain  of  the  same  width  as 
now,  in  order  to  increase  the  steadiness,  their  width  may 
be  increased  to  correspond  with  that  of  the  track,  (making 
it  10  or  11  feet  instead  of  the  present  8  or  9)  and  then 
they  will  be  as  steady  as  at  present,  but  be  much  more 
commodious  for  passengers,  (giving  space  to  sleep  and 
eat)  and  more  convenient  for  packing  bulky  freight,  as 
hay,  cotton,  lumber,  barrels,  cattle  on  the  hoof,  &c. 

The  preceding  are  the  advantages  belonging  to  the  cars  • 
those  gained  by  the  engines  are  still  greater. 

The  narrow  track  does  not  give  width  enough  to  make 
sufficiently  large,  and  to  arrange  to  the  greatest  advantage, 
the  various  parts  of  the  engine.  .With  their  usual  con- 
struction, the  highest  profitable  speed  for  maximum  loads 
(at  the  average  working  pressure  of  steam)  is  about  10 
miles  per  hour.  To  carry  the  same  load  at  twice  the 
speed,  it  would  be  necessary  to  double  the  quantity  of 


284  .     RAIL-ROADS. 

steam  generated  by  the  boiler,  and  therefore  to  double 
either  its  length  or  its  diameter.  The  length  of  its  flues 
cannot  be  advantageously  increased  ;  therefore  the  en  • 
largement  must  be  that  of  its  breadth.  To  effect  this, 
more  space  between  the  wheels  is  needed,  and  to  get  it,  a 
wider  track  is  required. 

Even  if  it  be  not  required  to  carry  great  loads  at  high 
speeds,  the  surface  of  the  boiler,  being  larger,  may  be 
less  intensely  heated,  and  will  therefore  last  longer. 

As  larger  driving  wheels  may  be  used  on  the  wide 
track,  their  adoption  will  enable  greater  speed  to  be  at- 
tained without  increasing  the  rate  of  motion  of  the  piston. 
The  expansive  force  of  steam  may  therefore  be  employed. 

The  larger  and  more  powerful  engines  will  do  more 
work,  with  no  more  men,  than  smaller  ones.  In  them 
there  is  therefore  the  same  economy  as  in  large  ships. 

OBJECTIONS  TO  THE  BROAD  GAUGE. 

More  ground  is  required  ;  and  the  excavations  and  em 
bankments  are  wider,  and  therefore  more  expensive. 

The  axles  must  be  heavier  to  have  the  same  strength  as 
before. 

There  is  an  increased  resistance  on  the  curves,  in  con- 
sequence of  the  increased  sliding  of  the  inner  wheels, 
which  is  equal  (as  was  seen  on  page  273)  to  the  differ- 
ence between  the  lengths  of  the  outer  and  inner  rails,  and 
therefore  proportional  to  the  difference  of  the  respective 
radii  of  the  curves. 

The  larger  engines  of  the  broad  gaug.^  roads  have  more 
power  than  is  generally  needed,  and  therefore  part  of  it  is 
practically  wasted. 

But  on  the  whole,  for  a  great  road,  the  advantages  of 
the  broad  gauge  would  indisputably  overpower  the  objec 


THEIR    GAUGE.  285 

tionsto  it,  if  it  were  not  for  the  evils  of  "  The  break  of 
gauge." 

THE    BREAK    OF    GAUGE. 

This  is  the  name  given  to  the  interruption  wHch  occurs 
whenever  a  road  of  broad  gauge  meets  one  of  narrow 
gauge,  and  which  renders  necessary  the  change  of  pas- 
sengers, baggage,  and  freight,  from  one  set  of  ^  cars  to  an- 
other, and  prevents  the  same  cars  being  run  through  without 
transhipment,  or  "  breaking  bulk."  Passengers  thus  suffer 
much  delay,  confusion,  and  discomfort ;  and  merchandise 
is  exposed  to  damage  and  risk  of  loss,  in  being  thus  changed 
from  one  car  to  another  midway  in  its  route,  besides  in- 
curring much  unnecessary  expense.  The  speedy  convey 
ance  of  troops  is  also  an  important  consideration  ;  for 
railroads  are  one  of  the  most  powerful  means  of  national 
defence,  enabling  an  army  to  be  concentrated  rapidly  at 
any  point  attacked  ;  but  their  value  for  this  purpose  would 
be  greatly  lessened  if  it  were  necessary,  at  some  "  break 
of  gauge"  on  the  route,  to  stop  and  lose  the  time  neces- 
sary for  transferring  the  troops,  with  their  artillery,  stores, 
&c.,  from  one  set  of  cars  to  another. 

Most  roads  belong  to  the  narrow  gauge  class.  In 
England  the  proportion  is  as  7  to  1  ;  there  being  in  op- 
eration, in  1846,  1901  miles  of  the  narrow  gauge,  and  only 
274  of  the  broad.  Every  new  road  of  broad  gauge,  con- 
necting with  a  narrow  one,  therefore  increases  the  evils 
of  the  break  of  gauge.  The  importance  of  lessening 
them  has  given  rise  to  various  contrivances  for  that  pur- 
pose. The  following  are  the  four  principal  remedies  pro- 
posed. 

1 .  Telescopic  axles.  The  axles  have  been  so  arranged 
that  one  portion  slides  in  the  other,  like  the  joints  of  a 


286  RAIL-ROADS. 

telescope,  so  that  the  distance  between  the  wheels  can  be 
so  adjusted  as  to  suit  either  the  broad  or  the  narrow  gauge. 
To  lessen  their  gauge,  the  catch  which  fastens  them  is 
loosened,  and  the  carriage  is  pushed  along  a  pair  of  rails, 
the  space  between  which  gradually  narrows  from  7  feet 
to  4  feet  8^  inches,  and  thus  the  wheels  of  the  carriage 
are  gradually  forced  nearer  to  each  other.  To  widen 
their  gauge  the  operation  is  reversed.  But,  besides  the 
expense  of  the  alteration,  there  is  a  resulting  unsteadiness, 
and  consequent  liability  to  danger. 

2.  Low  trucks  on  the  broad  gauge  roads  may  have  rails 
laid  on  them  4  feet  8^  inches  apart,  upon  which  the  nar- 
row gauge  cars,  may  be  run,  and  thus  be  carried  on  the 
broad  roads.     But  this  contrivance  raises  the  centre  of 
gravity,  making  the  whole  top-heavy ;  and  adds  so  much 
extra  dead-weight  to  the  load.    Besides,  it  does  not  provide 
for  conveying  the  broad  gauge  cars  on  the  narrow  roads. 

3.  Shifting  car-bodies  for  passengers  have  been  pro- 
vided, which  could  be  swung,  by  powerful  cranes,  from 
one  set  of  wheels  to  another ;  and  Moveable  boxes,  to  re- 
ceive merchandise,  have  been  made  of  such  a  size,  that 
one  should  be  carried  on  a  narrow  gauge  track,  and  two 
on  a  broad  one. 

4.  Extra  rails  have  been  laid,  so  that  the  same  road 
could  be  used  for  both  classes  of  cars  ;  a  pair  of  narrow 
gauge  rails  being  laid  within  the  broad  ones,  or  only  a 
single  rail  being  laid,  so  as  to  be  4  feet  81  inches  from 
one  of  the  broad  gauge  rails.     But,  besides  the  expense 
of  these  arrangements,  there  would  be  increased  danger 
at  the  crossings. 

All  these  remedies  are  imperfect ;  and  the  "  break  of 
gauge"  seems  to  be  an  evil  for  which  there  is  no  cure,  ex 
cept  in  destroying  its  cause. 


THEIR    GAUGE.  287 

The  Royal  Commission,  appointed  by  the  British  Par 
liament,  in  1845,  to  investigate  this  subject,  made  an  eiab« 
orale  report  in  1846,  and  sum  up  as  follows  : 

"1.  As  regards  the  safety,  accommodation,  and  conve 
nience  of  the  passengers,  no  decided  preference  is  due  to 
cither  gauge  ;  but  on  the  broad  gauge  the  motion  is  gen 
erally  more  easy  at  high  velocities. 

"  2.  In  respect  of  speed,  we  consider  the  advantages 
are  with  the  broad  gauge ;  but  we  think  the  public  safety 
would  be  endangered  in  employing  the  greater  capabili- 
ties of  the  broad  gauge  much  beyond  their  present  use, 
except  on  roads  more  consolidated,  and  more  substan- 
tially and  perfectly  formed,  than  those  of  the  existing 
lines. 

"  3.  In  the  commercial  case  of  the  transport  of  goods, 
we.  believe  the  narrow  gauge  to  possess  the  greater  con- 
venience, and  to  be  the  more  suited  to  the  general  traffie 
of  the  country. 

"  4.  The  broad  gauge  involves  the  greater  outlay ;  and 
we  have  not  been  able  to  discover,  either  in  the  mainten- 
ance of  way,  in  the  cost  of  locomotive  power,  or  in  the 
other  annual  expenses,  any  adequate  reduction  to  compen- 
sate for  the  additional  first  cost." 

They  recommend  "  that  the  gauge  of  four  feet  eight 
inches  and  a  half,  be  declared  by  the  legislature  to  be  the 
gauge  to  be  used  in  all  public  railways  now  under  con- 
struction, or  hereafter  to  be  constructed,  in  Great  Britain." 
They  add,  that  "  great  commercial  convenience  would  be 
obtained  by  reducing  the  gauge  of  the  present  broad 
gauge  lines  to  the  narrow  gauge  ;"  and  "  think  it  desirable 
ihat  some  equitable  means  should  be  found  of  producing 
such  entire  uniformity  of  gauge,  or  of  adopting  such  other 
course  as  would  admit  of  the  narrow  gauge  carriages 
19 


288  RAIL-ROAD?. 

passing,  without  interruption  or  danger,  along  the  broad 
gauge  lines." 

The  final  conclusion  seems  to  be  that,  if  all  railroads 
were  now  to  be  constructed  anew,  a  gauge  of  five  and  a 
half,  or  six  feet,  would  be  considered  most  desirable  ;  but 
that  the  evils  of  a  "  break  of  gauge"  are  so  great,  in  the 
present  preponderance  of  narrow  gauge  roads,  as  to  over- 
balance the  disadvantages  of  the  narrow  gauge  ;  which 
should  therefore  be  adopted  by  all  future  railroads  which 
are  to  connect  with  others. 

WIDTH    OF    ROAD-BED. 

When  the  gauge  has  been  decided  upon,  the  necessary 
width  of  the  roadway  can  be  determined.  When  the  road 
has  a  double  track,  the  middle  space  between  the  two 
pairs  of  rails,  for  convenience  and  safety,  should  not  be 
less  than  six  feet.  The  side-spaces,  outside  of  the  rails, 
should,  for  safely,  be  a  little  more  than  the  width  of  the 
track,  particularly  on  embankments  ;  so  that  if  the  engine 
gets  off  the  track,  it  may  still  remain  upon  the  bank.  This 
width  also  gives  greater  stability  to  the  embankment  and 
to  the  rails  laid  upon  it,  diminishing  their  liability  to  be 
disturbed  by  slips.  These  side-spaces  are  from  5  to  8 
feet  on  different  railways.  They  should  be  greatest  on 
roads  where  great  velocity  is  adopted  ;  on  high  embank 
ments  ;  and  on  the  outside  of  curves.  They  will  of 
course  be  less  in  tunnels,  viaducts,  bridges,  &c. 

The  total  width  of  the  road-bed  of  a  railroad,  with  nar- 
row gauge  and  double  track,  will  therefore  be  6  +  2  (4f ) 
-f-2x6=  27^  feet.  In  excavations,  the  widths  of  the 
ditches  on  each  side  must  be  added. 

The  total  width  of  a  double  track  railroad  is  usu- 
ally about  28  feet  in  excavations  and  24  feet  in  em- 


THEIR    WIDTH.  299 

banluncnts  Single  track  railroads  are  about  ten  feet 
less,  say  IS  and  14  feet.  These  dimensions  are  used 
\vlien  great  economy  is  required,  and  are  increased 
for  wet  cuts  and  high  banks. 

If  it  be  proposed  to  lay  only  a  single  track  at  first,  and 
subsequently  to  add  a  second  one,  the  cuttings  and  fillings 
should  always  be  made  at  first  of  the  full  width  for  a 
double  track  ;  for  the  extra  expense  of  the  additional  width 
is  but  a  small  proportion  of  the  whole,  and  a  narrow  cut 
or  bank,  is,  from  the  want  of  room  for  the  carts,  &c.  to 
pass,  worked  much  more  disadvantageous^,  and  therefore 
much  more  expensively,  than  a  wide  one.  .  If  an  embank 
ment  be  subsequently  widened,  the  new  portion  will  not 
adhere  to  the  side  of  the  old  one  without  forming  the  lat- 
ter into  steps  ;  and  in  widening  a  rock  excavation,  a  single 
blast  might  render  the  road  impassable  for  many  hours. 

The  other  subjects  properly  belonging  to  the  "  Cross- 
section,"  such  as  the  elevation  of  the  outer  rail  on  a  curve, 
&c.,  will  be  more  advantageously  examined  under  the 
head  of  "  Superstructure." 

Very  narrow  gauge  railroads  have  been  worked  with  great  success,  and  their 
use  is  increasing.  The  best  known  of  these  is  the  Festiniog  Railway  in  North 
Wales.  The  gauge  is  only  23J  inches.  A  heavy  traffic  is  carried  on  over  this 
road,  and  the  profit?  yield  a  large  percentage  on  the  original  outlay.  A  3J  feet 
gauge  has  been  successfully  used  in  Norway,  Sweden,  Belgium,  and  other 
places. 

It  seems  advisable  to  make  4  ft.  8f  in.  the  maximum  width,  and  to  adopt  a 
much  narrower  gauge  where  the  traffic  is  limited.  On  the  Great  Western  Rail- 
way of  England  the  famous  7  ft.  gauge,  introduced  by  Brunei,  is  being  aban- 
doned :  a  large  part  of  it  having  already  been  replaced  by  the  4  ft.  8J  in.  gauge. 
Several  wide  gauge  roads  in  the  United  States  have  been  changed  tc  a  4  ft.  84 
111.  gauge. 


2<JO  RAIL-ROADS. 

II.     THE  LOCATION  OF  RAILROADS. 

The  location  of  railroads  is  guided  by  the  same  princi- 
ples as  that  of  common  roads,  and  made  in  similar  man- 
ner ,  but  the  greater  importance  to  railroads  of  straight 
lines  and  easy  grades,  as  has  been  shown  in  the  preceding 
section,  justifies  and  requires  ;•  much  greater  expenditure  in 
the  surveys  which  seek  the  attainment  of  these,  and  in 
the  excavations,  embankments,  and  bridges  by  which  they 
are  secured.  The  minor  undulations  of  the  country  are 
disregarded,  for  they  can  be  readily  overcome  by  the  cut- 
tings and  fillings  which  will  be  demanded  by  any  traffic 
which  is  important  enough  to  need  a  railroad  for  its  ac- 
commodation ;  and  straightness  is  the  first  object :  where 
a  common  road  should  go  around  a  hill,  a  railroad  should 
cut  through  it.  For  this  reason,  the  compass,  or  some 
other  angular  instrument,  usually  takes  the  lead  in  the 
location,  and  is  followed  by  the  level.  Upon  the  rough 
plot  of  the  survey,  curves  are  pencilled  in,  their  centres 
and  radii  are  determined,  and  then  they  are  laid  out  on  the 
ground,  being  corrected,  if  necessary,  by  calculation  or 
by  trial,  till  they  pass  through  the  desired  points.  The 
important  calculations  for  excavation  and  embankment  are 
identical  with  those  of  common  roads  ;  but  the  estimate 
must  include  the  new  items  of  superstructure,  of  engines 
cars,  &c.,  which  are  to  be  presently  examined. 

In  examining  the  comparative  merits  of  two  rival 
routes,  the  relative  importance  of  distance  and  grade 
or  shortness  and  steepness,  must  be  determined  by  the 
considerations  given  on  pages  276 — 281.  To  determine 
which  is  the  least  objectionable  in  amount  of  curvature, 
calculate  the  angular  deflection  of  each  curve,  as  indi- 
cated on  p.  274.  The  sum  of  all  of  these  on  each  line 
will  be  its  total  deflection,  and  the  proper  standard  for 
comparing  it  with  others. 


FORMING    HIE    ROAiJ-BJSD.  29  J 

III.    THE  CONSTRUCTION  OF  RAILROADS. 

The  two  principal  divisions  of  this  part  of  the  subject 
are — "  Forming  the  Road-bed,"  (which  corresponds  to  the 
general  "  Construction"  of  common  roads) ;  and  the 
"  Superstructure,"  which  includes  the  Rails,  and  their 
supports,  ties,  &c. 

1.  FORMING  THE  ROAD-BED. 
EXCAVATIONS. 

The  Excavations  on  railroads  are  often  of  much  greatel 
depths  than  are  ever  necessary  on  common  roads,  the 
extra  expense  being  amply  repaid  by  the  advantages  of 
the  easier  grades  and  straighter  lines  thereby  attained. 
There  is  an  excavation  (in  sand)  on  one  English  railway, 
110  feet  deep;  and  on  another,  16,000,000  cubic  yards 
of  material  were  removed.  The  thorough  drainage  of 
these  excavations  by  ditches,  cross-drains,  &c.,  is  of  the 
highest  importance.  Their  sides  often  need  to  be  sup- 
ported by  retaining  walls,  in  order  to  make  steeper  slopes 
possible,  and  thus  to  lessen  their  top  width,  when  they 
pass  through  valuable  ground.  Sometimes  these  retaining 
walls  are  supported  by  iron  beams,  or  flat  arches,  extend- 
ing across  the  railway  at  a  sufficient  height  to  clear  the 
engines.  In  one  remarkable  cutting,  60  feet  deep,  the 
upper  portion  of  it  was  rock,  but  the  lower  looser  matter. 
If  the  whole  cutting  had  been  extended  upwards,  with 
such  side  slopes  as  the  looser  and  lower  portion  required, 
it  would  have  been  more  than  200  feet  wide  at  its  top, 
and  would  have  involved  very  great  expense  in  the  re- 
moval of  so  large  an  amount  of  rock.  The  sides  of  the 
cutting  were  therefore  made  nearly  perpendicular,  and  the 


292  BAIL-BOADS. 

loose  strata  at  the  bottom  were  supported  by  retaining 
walls,  carried  up  till  they  reached  the  solid  rock.  Such 
are  some  of  the  ingenious  expedients  rendered  necessary 
by  the  gigantic  constructions  of  modern  railroads. 

The  side  slopes  will  depend  upon  the  material  through 
which  the  cutting  is  made.  For  common  earth  they  are 
usually  1£  to  1,  although  in  deep  cuts  they  should  be  2 
to  1.  It  is  sometimes  economical  to  make  the  slopes  at 
first  as  steep  as  they  will  stand,  and  remove  the  surplus 
earth  after  the  track  is  laid.  Clay  slopes  are  very  trou- 
blesome. Some  that  have  stood  at  first  at  2  to  1,  have 
finally  slipped  until  they  were  6  to  1.  Slope  walls  have 
been  used  in  such  soil,  as  being  more  economical  than 
taking  out  the  requisite  amount  of  earth  to  secure  stabil- 
ity to  the  banks.  It  has  been  observed  that  the  mass  of 
earth  which  slides  out  of  a  clay  slope  leaves  the  bank 
with  a  concave  face.  It  will  then  be  better  to  make  the 
original  excavation,  so  as  to  leave  the  slopes  with  this 
curved  batir. 

In  making  long,  deep  cuts,  the  bottom  should  be  left 
so  as  to  slope  up  from  both  ends  toward  the  centre,  to 
secure  drainage  while  the  work  of  excavating  is  going 
on.  The  bottom  can  be  taken  out,  down  to  the  desired 
grade  of  the  finished  work,  after  the  main  portion  of  the 
earth  has  been  removed.  When  the  cut  is  very  deep,  the 
work  can  be  pushed  forward  more  rapidly  by  working  in 
tiers  or  stories,  keeping  the  upper  one  in  advance  of  the 
lower  one. 

Ditches  should  always  be  dug  on  the  surface,  a  few 
feet  back  from  the  edge  of  the  cutting,  to  prevent  the 
surface  water  from  running  down  the  side  slopes. 


TUNNELS.  293 


The  depth  of  an  excavation  frequently  renders  a  Tunnei 
more  economical.  In  constructing  one,  the  centre  line  of 
the  road  must  be  set  out  with  very  great  accuracy  upon 
the  surface  of  the  ground,  (by  a  Transit  instrument)  and 
"  shafts"  sunk  at  proper  intervals  along  this  line.  The 
excavations  are  made  by  "  headings,"  or  "  drifts,"  from 
shaft  to  shaft,  and  to  the  open  ends  of  the  tunnel.  The 
material  excavated  is  raised  through  these  shafts,  which, 
after  the  completion  of  the  tunnel,  serve  as  ventilators. 
Their  distances  apart  should  be  from  500  to  1000  feet. 
If  the  material  be  earth,  or  stratified  rock,  the  crown  of 
the  tunnel,  and  its  sides,  must  be  supported  by  a  brick 
arch,  and  the  excavation  kept  only  a  few  feet  in  advancf 
of  the  completed  arch. 

The  height  of  tunnels,  in  the  clear,  varies  on  the  Eng 
lish  railways  from  17  to  30  feet,  and  the  width,  for  a 
double  track,  from  22  to  30  feet.  The  average  sectional 
area  in  the  clear,  is  450  square  feet :  when  an  arch  is 
required,  the  excavation  would  contain  about  700  square 
feet.  The  cost  per  lineal  foot  of  the  English  railway 
tunnels,  has  ranged  from  $30  to  8150.  If  sufficient  time 
had  been  allowed,  they  could  generally  have  been  executed 
for  860  per  lineal  foot.  A  number  in  England  are  over  a 
mile  in  length,  and  one  is  more  than  a  mile  and  three 
quarters. 

The  greatest  work  of  the  kind  is  under  the  Alps,  at 
Mount  Cenis,  connecting  Modane,  in  France,  with  Bar- 
donneche,  in  Italy,  and  is  seven  miles  and  one  thousand 
and  forty-four  yards  in  length.  No  shafts  could  be  used, 
as  the  mountain  rose  rapidly  from  both  sides,  and  there 
were  no  depressions.  The  tunnel  is  one  mile  below  the 
summit  of  the  mountain. 

The  expense  of  construction  was  borne  by  the  French 
and  Italian  governments,  each  paying  in  proportion  to 
the  length  of  tunnel  lying  in  their  territory. 


294  BAIL-BOADB. 


EMBANKMENTS. 

The  embankments  of  railroads  demand  the  use  of  every 
possible  precaution  to  ensure  their  solidity  ;  not  only  on 
account  of  their  size,  but  because  the  vibrations  imparted 
to  them  by  the  passing  trains,  greatly  increase  their  ten- 
dency to  slip.  The  expense  and  time  required  to  form 
them  in  layers,  as  recommended  on  page  166,  often  forbid 
the  adoption  of  that  method.  They  are  usually  con- 
structed by  raising  them  to  their  full  height  at  one  end, 
and  so  carrying  them  onward.  Temporary  rails  are  laid 
along  the  bank,  and  extended  with  it,  and  on  them  wagons, 
containing  each  about  3  cubic  yards,  are  drawn  by  horses, 
or  by  locomotive  engines,  if  the  distance,  or  "  lead,"  be 
great. 

It  has  been  ascertained  that,  contrary  to  the  usual  the- 
ory and  practice,  the  quantity  of  work  which  can  be  done 
on  an  embankment  so  made,  and,  consequently,  the  time 
which  will  be  required  for  its  completion,  does  not  de- 
pend on  the  area  of  the  face  of  the  cutting  which  supplies 
it,  or  on  the  number  ol  wagons  which  can  be  filled  in  it 
together ;  but  on  their  rate  of  speed,  and  on  the  number 
of  them  which  can  be  emptied  in  a  given  time  over  the 
head  of  the  embankment,  to  the  top  width  of  which  this 
element  is  proportional.  The  number  of  wagons  drawn 
together  in  a  "  set,"  should  increase  or  decrease  with  the 
length  of  the  "  lead,"  and  the  breadth  of  the  end  of  the 
bank  ;  and  the  number  of  "  sets"  should  be  increased  at 
certain  exact  periods  in  the  progress  of  the  work,  which 
are  susceptible  of  mathematical  determination.* 


*  These  points  are  very  clearly  and  fully  examined  in  "  l&vt  of  Ex- 
cavation and  Embankment  on  Railways,"  London,  1840. 


EMBANKMENTS.  295 

When  the  road  crosses  a  swamp,  the  banks  may  be 
formed  as  explained  on  pp.  168,  9.  A  railroad  is  carried 
across  the  Montezuma  swamp,  N.  Y.,  by  spreading  the 
pressure  over  a  large  surface,  by  means  of  a  wooden  plat- 
form. On  another  railroad  a  spreading  base  was  secured, 
to  carry  a  bank  across  a  swamp,  by  placing  trees  and 
brush  under  the  bank,  at  right  angles  to  the  line  of  the 
road,  and  extending  for  some  distance  beyond  the  foot 
of  the  side  slopes.  Water  should  never  be  allowed  to 
stand  within  three  feet  of  the  top  of  the  bank. 

When  a  railroad  passes  through  a  wooded  swamp,, 
where  no  materials  for  embankment  are  at  hand  a  cheap 
and  efficient  substitute  will  be  formed  by  a  series  of  tim- 
ber trusses.  Piles  of  15  inches  diameter,  not  sharpened, 
are  driven  so  as  to  form  two  lines,  at  a  distance  from  each 
other  equal  to  the  width  of  the  railroad.  Transverse  ties 
are  fastened  across  their  tops,  which  are  braced  by  in- 
clined struts,  the  lower  ends  of  which  abut  against  short 
piles.  Longitudinal  timbers  are  laid  on  the  heads  of  the 
piles  to  carry  the  rails.  Various  combinations  of  the 
trusses  are  employed,  according  to  the  height  of  the  su- 
perstructure above  the  surface  of  the  ground.  After  the 
railroad  has  been  thus  constructed,  it  may  be  gradually 
banked  up  to  the  level  of  the  rails,  by  taking  advantage 
of  its  facilities  of  transportation,  to  bring  earth  from  a 
distance  to  the  places  where  it  is  needed. 

The  side-slopes  of  both  the  excavations  and  the  em- 
bankments should  be  sown  with  grass  seed, .or  sodded,  as 
directed  in  the  construction  of  roads.  Some  dee,p  cut- 
tings on  the  English  railways,  have  been  planted  with 
flowers,  shrubs,  and  trees  ;  an  improvement  as  delightful 
to  the  passenger  and  therefore  profitable  to  the  proprietors 
of  the  road,  as  it  is  beneficial  to  the  permanence  of  the 
slopes. 


BAIL-KOADS. 


BALLASTING. 

The  tops  of  the  embankments,  and  the  bottoms  of  the 
excavations,  are  brought  to  a  height  call  d  the  "  Forma- 
tion level,"  about  two  feet  below  the  intended  level  of  the 
rails,  and  there  shaped  with  a  fall  from  the  middle  to  each 
side,  as  in  common  roads,  in  order  to  drain  off  the  water 
which  falls  upon  them.  The  remaining  space  of  two 
feet  (more  or  less,  according  to  circumstances)  is  filled  up 
with  "ballast," 

There  are  four  objects  in  using  ballast : 

1.  To  spread  the  bearing  of  the  sleepers  over  a  large 
surface  of  the  ground. 

2.  To  keep  the  track  in  place. 

3.  To  secure  drainage. 

4.  To  give  a  medium  elasticity. 

It  is  composed  of  some  porous  material,  such  as  gravel, 
broken  stones,  quarry  rubbish,  cinders',  etc.,  through 
which  the  water  of  rains  can  readily  pass.  Burnt  clay 
has  been  used  in  alluvium  countries.  It  should  be  laid 
on  rock  as  well  as  earth,  and  should  extend  one  or  two 
feet  beyond  the  ends  of  the  ties  in  cuttings,  and  be  of  the 
full  width  of  the  embankments. 

Upon  this  "  ballast"  are  laid  the  supports  of  the  rails. 
Without  this  precaution,  the  water  absorbed  by  the  earthy 
materials  of  the  road-bed  would  render  it  soft  and  spongy 
in  ordinary  weather,  and  by  freezing  in  winter  would  dis- 
turb the  position  and  the  levels  of  the  rails.  On  many 
American  railroads  the  neglect  of  this  safeguard  against 
the  effects  of  our  Northern  winters  renders  them  very 
unsafe  at  high  velocities  in  the  early  spring,  when  the 
frost  is  coming  out  of  the  ground.  Ships'  ballast  was 
first  used  for  this  purpose  on  the  early  railroad  at  New- 
castle, and  from  this  circumstance  the  substitutes  have 
retained  the  original  name. 


SUPERSTRUCTURE.  297 


2.  THE  SUPERSTRUCTURE. 

Under  this  head  will  be  considered  the  best  forms  and 
weights  of  rails,  whether  supported  at  intervals  (in  chairs, 
on  stone  blocks  or  wooden  cross-sleepers)  or  on  continuous 
bearings  for  their  whole  length  ;  and  their  proper  arrange 
ment,  inclination,  elevation,  &c.,  when  laid. 

RAILS    SUPPORTED    AT    INTERVALS. 

When  rails  are  supported  only  at  intervals,  on  props, 
like  a  bridge  on  piers,  they  are  liable  to  be  depressed  be- 
tween these  supports  by  the  heavy  loads  which  pass  over 
them.  It  is  therefore  very  important  to  give  them  such  a 
shape  as  will  secure  the  greatest  strength  with  the  least 
quantity  of  material.  The  form  indicated  by  theory,  and 
originally  adopted  in  practice,  is  that  called  "  fishbellied," 
from  the  rounded  profile  of  its  under  side.  A  rail  of  such 

Fig.  121. 


a  form,  will  have  more  power  to  resist  deflection  than  a 
straight  one  of  the  same  weight,  in  the  proportion  of  1 1 
to  9.*  But  wliatever  the  theoretical  advantages  of  this 
form,  its  inconvenience  in  practice,  owing  to  its  requiring 
a  higher  support,  which  is  therefore  less  steady,  has  caused 
it  to  be  generally  discarded. 

The  forms  now  used  are  all  varieties  of  the  parallel  or 
straight  rail,  in  which  the  top  and  bottom  are  parallel, 
and  which  has  the  same  cross-section  at  all  parts  of 


*  Lecount,  p.  110.     Barlow  doubts  this. 


298 


RAIL-ROADS. 


its  length.  Usually  the  rail  is  thinner  through  its  mid- 
dle than  at  its  top  and  base.  The  various  forms  are  named 
the  T  rail,  the  H  rail,  the  hour-glass  rail,  &c.  from  the 
shape  of  their  cross-section.  The  popular  division  of 
rails  is  into  the  "  Plate  rail,"  and  the  "  Edge  rail ;"  the 
latter  including  all  the  varieties  just  mentioned. 

The  best  form  of  the  parallel  rail  was  in-  F'g- 122- 
vestigated  by  Professor  Barlow,  in  behalf  of 
the  London  and  Birmingham  Railway  Com- 
pany, and  Fig.  122  shows  the  section  of  the 
rail  which  he  found  to  possess  the  greatest 
strength  with  the  least  material,  the  bottom  web 
being  much  smaller  than  the  head. 

But  a  double  headed,  or  H  rail,  as  shown     Fig.  123 
in  Fig.  123,  with  its  top  and  base  of  the  same 
size  and  shape,  is  now  generally  preferred  in 
England.       Professor   Barlow  considers   this 
shape    to    be   inferior  in  strength  and   conve- 
nience in  fixing,  its  broader  bearing  to  be  of 
no  advantage,  and  the  proposed  plan  of  turn- 
ing it  over,  when  the  upper  table  is  worn  down,  to  be  im 
practicable ;  but  still  it  is  found  preferable  in  practice,  as 
enabling  the  best  side  to  be  selected,  as  being  more  easily 
keyed  in  its  chair,  and  as  having  a  broader  bearing. 


The  favorite  form  in  this  country 
is  shown  in  Fig.  124.  The  follow- 
ing dimensions  are  recommended: 
height,  4  in.,  width  of  bottom,  4 
in.,  width  of  head,  2f  in.,  thick- 
ness of  vertical  web,  -fa  in. 


Fig.  124. 


Steel  rails  (usually  Bessemer  steel)  are  coming  into  almost  universal  use, 
owing  to  their  creator  durability  and  strength,  although  the  first  cost  is  much 
greater. 


FORM    AND    WEIGHT    OF    RAILS.  299 

The  form  of  the  rail  being  decided  upon,  its  tceight,  on 
which  its  strength  depends,  is  next  to  be  determined. 
The  weight  is  expressed  by  the  number  of  pounds  in  a 
lineal  yard.  Its  minimum  may  be  determined  thus.  A 
certain  breadth  is  necessary  for  the  bearing  surface  of  the 
rail,  that  the  wheel  may  run  upon  it  without  being 
grooved.  2|  inches  seems  the  minimum  for  this.  The 
minimum  breadth  is  desired,  in  order  ll^at  as  much  as 
possible  of  t'ue  material  may  be  put  in  to  depth,  the 
strength  being  as  the  simple  breadth,  but  as  the  square 
of  the  depth.  The  minimum  depth,  to  resist  abrasion 
and  exfoliation,  is  1^  inches.  This  gives  a  sectional  area 
of  2^  x  1|  inches  =  3. 75,  or,  say  4  inches,  which  corre 
spends  to  36  Ibs.  to  the  yard.  This  is  then  the  minimum 
weight  permissible,  when  the  rail  is  supported  throughout 
its  whole  length  ;  but  if  supported  at  intervals  it  must 
have  much  greater  weight  and  strength,  their  degree  de- 
pending on  the  distance  between  its  points  of  support. 

This  distance  has  varied  from  3  to  6  feet.  It  is  now 
generally  made  less  than  3  feet.  For  Professor  Barlow's 
form  of  rail,  Fig.  122,  with  a  strength  of  7  tons,  the 
weight  should  be  51  Ibs.  per  yard,  for  a  bearing  of  3  feet. 
To  attain  the  same  strength  with  a  bearing  of  6  feet,  the 
weight  should  be  79  Ibs.  per  yard.  But  the  deflection  of 
the  rail  with  3  tons,  which  in  the  former  case  is  only  .024 
inch,  in  the  latter  is  .082  inch.  Thus  the  longer  bearings, 
when  equally  strong  with  the  shorter,  are  much  less  stiff, 
and  therefore  much  inferior  to  them.  The  effect  of  any 
depression  under  a  passing  load  is  that  the  engine,  at 
slow  speeds,  after  sinking  into  it,  has  an  inclined  plane  to 
ascend,  and  at  high  speeds  it  leaps  over  the  hollow,  and 
strikes  with  great  violence  upon  the  other  side  of  it.  A 
rail  having  been  bent  half  an  inch,  and  then  covered  with 


300  RAIL-ROADS. 

paint,  an  engine  with  a  train  of  cars  was  run  over  it,  and 
none  ;>f  the  wheels  touched  the  paint  for  a  space  of  22 
inches.*  Strength  to  resist  deflection  is  therefore  as  im- 
portant to  a  rail  as  its  strength  to  bear  weights.  The 
latter  should  be  double  the  mean  strain  or  load.  The 
former  should  not  admit  of  a  depression  under  a  passing 
load  of  more  than  Tf  ^  of  an  inch. 

The  weight  of  rails  has  been  yearly  increasing.  The 
first  rails  laid  on  the  Liverpool  and  Manchester  railway 
were  only  35  Ibs.  to  the  yard  ;  they  have  been  succes- 
sively replaced  by  rails  weighing  50,  65,  and  75  Ibs.  to 
the  yard.  The  rail  shown  in  Fig.  123  weighs  75  Ibs.  to 
the  yard,  with  bearings  3  feet  9  inches  apart.  Its  whole 
depth  is  5  inches  ;  the  top  and  base  are  2|  inches  ;  and 
the  thickness  of  the  middle  rib  is  about  |  of  an  inch.  On 
the  Massachusetts  railroads  the  rails  weigh  from  56  to  60 
Ibs.  per  yard,  and  rest  on  cross-sleepers,  2  feet  G  inches 
apart  ;  the  weight  on  a  driving  wheel  being  from  5,000  to 
8,000  Ibs.  English  rails  weigh  from  50  to  80  pounds  per 
yard,  and  German  rails  from  50  to  70  pounds.  Steel  rails 
can  be  made  much  lighter  than  iron  ones,  and  yet  have 
the  same  strength.  The  steel  rails  on  the  Hudson  Eiver 
Railroad  weigh  from  56  to  60  pounds  to  the  yard. 

The  rails  are  usually  rolled  in  lengths  of  from  12  to  20 
feet.  Their  ends  have  received  various  shapes.  Square 
or  butt  ends,  Fig.  125,  are  generally  Fig.  125. 

preferred,    but    cause    considerable    ^  If  ( 

shock  to   the   wheel.     The  half-lap  Fig.  126. 

joints,   Figs.    126   and    127,    retain    F  ^         {* 

their  positions  better,  but  weaken  the  F-     127 

ruil.    The  form  shown  in  Fig.  128  is     j  -  ILJJ  -  \ 


«  Lecount,  p.  89. 


CHAIRS.  30} 

recommended  when  trains  run  Fig.  128. 

on  each  track  in  only  one  di-    t .  H^  -    -1 

rection,  (as  indicated  by  the  ar-      ^^ 
row)  so  that  they  never  meet 

the  points  of  the  rails.*  $  — 7/  / 

Between  the  ends  of  two  successive  lengths-  of  rails,  a 
space  must  be  left  to  allow  for  their  expansion  by  heat. 
The  expansion  of  a  fifteen  feet  rail  may  be  taken  at  -g^ 
of  an  inch  for  each  degree  of  Fahrenheit,  or  |  inch  for 
100°.  If  the  rails  were  laid  in  the  coldest  weather,  a 
space  of  one-eighth  of  an  inch  should  therefore  be  left 
between  their  ends.  The  force  with  which  iron  expands 
is  from  6  to  9  tons  per  square  inch  of  section,  which  cor- 
responds to  10  Ibs.  to  the  yard  ;  so  that  the  rail  of  70 
<bs.  expands  with  a  force  of  about  fifty  tons. 


The  rails  may  be  fastened  directly  to  their  supports, 
or  have  their  ends  also  held  by  "  chairs,"  spiked  to  the 
blocks  or  cross-sleepers.  The  chairs  are  generally  of 
cast  iron,  and  weigh  from  20  to  30  Ibs.  They  are  cast 
in  one  piece,  consisting  of  a  bottom  plate,  and  two  side 
pieces,  between  which  the  rail  passes,  its  under  surface 
being  about  an  inch  above  the  block.  The  opening  of  the 
chair  must  be  as  wide  as  the  lower  part  of  the  rail,  in  or- 
der that  it  may  be  removed  and  replaced  without  disturb- 
ing the  chair.  Keys  of  wood,  or  of  iron,  must  therefore 
be  employed  to  fill  up  this  opening,  and  to  hold  the  rail 
firmly  in  the  chair,  but  without  offering  any  resistance  to 
its  longitudinal  motion  in  expansion  and  contraction. 
On  the  Liverpool  and  Manchester  Railway  the  chair 

*  Lecount,  |±>.  112. 


RAIL-ROADS. 


Fig.  130. 


Fig.  131 


shown  in  Fig.  129,  was  employ-  FiS-  129- 

ed      The  rail  has  on  one  side  of 

its  bottom  a  projecting  rib  which 

enters  a  notch  in  the  chair,  and 

another  notch  on  the  other  side 

receives  an   iron  pin.     To  prevent  its  getting  loose,  that 

end  of  the  pin  which  enters  first  may  be  split,  and  opened 

when  driven  home. 

Another  good  form,   shown  in 

Fig.    130,  was  invented  by  Mr. 

Robert  Stephenson.    In  it  the  rail 

is  confined  by  two  bolts  with  an- 
gular ends,  which  enter  a  small 

score  in  the  rail,  and  are  keyed 
home  by  iron  keys  with  split  ends. 
Fig.  131  represents  Mr.  Barlow's 
patent  hollow  iron  key  applied  to 
fasten  a  double-headed  parallel 
rail. 

Wooden  keys,  of  similar  shape, 
but  solid,  have  been  much  used,  owing  to  the  great  facili- 
ty which  they  offer  of  being  tightened  and  replaced.  They 
should  be  kiln-dried,  cut,  and  compressed  by  hydraulic 
pressure,  so  that  by  their  swelling,  after  being  driven  in, 
they  may  hold  the  rail  very  tightly. 

Tne  chair  used  for  the 
inverted  T  rail  is  shown 
in  Fig.   132.      It  is 
inches  wide,  8£  long,  \ 
high,  and  weighs  24  Ibs. 

Generally  the  chairs  are 
placed  only  at  the  ends  of  the  rails,  which  are  fustenedtc 
the  intermediate  supports  by  spikes  with  bent  heads. 


STOXE  BLOCKS.  303 

The  most  perfect  arrangement  for  joining  the  rails, 
and  for  keeping  them  at  the  same  level  and  in  line  with 
each  other,  is  "  fish-plates."  These  are  iron  plates,  bolted 
on  each  side  of  the  rails  at  the  joints. 

They  should  be  at  least  20  inches  long,  fit  closely  be- 
tween the  head  and  base  of  the  rail,  and  be  in  contact 
with  the  vertical  web  throughout  the  entire  length  of  the 
plates. 

They  should  be  secured  by  four  -f-  inch  bolts.  The 
holes  in  the  plates  and  rails  should  be  oblong,  to  allow 
for  the  expansion  and  contraction  caused  by  the  changes 
of  temperature. 

STONE    BLOCKS. 

Stone  blocks  imbedded  in  the  ballasting,  have  been  till 
iately  the  principal  supports  employed  on  the  English 
railways.  They  are  usually  blocks  of  granite,  or  whin 
stone,  two  feet  square  and  one  foot  deep.  The  custom- 
ary distances  between  their  centres  have  been  noticed  on 
page  271.  They  are  sometimes  placed,  as  in  Fig.  183, 
with  their  sides  parallel  to  the  line  of  the  road  ;  and  some- 
times diagonally,  as  in  Fig.  134. 

Fig.  133.  Fig.  134. 


Both  plans  have  their  advocates.  The  former  position 
offers  more  resistance  to  motion  in  the  line  of  the  road.* 
The  latter  is  less  stable,  but  is  more  convenient  for  pack- 
ing the  ballast  around.  Circular  blocks  have  been  pro- 


»  In  the  proportion  of  1728  to  1629      For  the  investigation,  see  Lo 
count,  p.  93 

20 


304  RAIL-ROADS. 

posed  in  order  to  get  equal  resistance  in  all  directions,  but 
the  gain  would  not  equal  the  extra  expense. 

The  blocks  must  be  very  carefully  set  precisely  level, 
since  even  a  quarter  inch  difference  in  3  feet,  would 
create  an  inclined  plane  of  1  in  144,  or  37  feel  to  the  mile. 

On  curves  the  blocks  on  each  side  of  the  road  must  be 
connected  by  iron  tie-rods,  that  the  exterior  ones  may  not 
be  pressed  outward  by  the  centrifugal  force  of  the  cars. 

Stone  blocks  have  been  also  laid  transversely,  with  the 
advantage  of  preserving  the  gauge  of  the  road,  but  with 
the  evils  of  great  rigidity,  hardness,  and  jolting. 

WOODEN    CROSS-SLEEPERS. 

Transverse  or  cross-sleepers  of  wood  are  now  consid 
ered  preferable  to  stone  blocks  for  many  reasons.  They 
tie  the  rails  together  and  preserve  their  parallelism,  and 
also  make  the  road  less  rigid  and  more  elastic  than  the 
stone,  and  therefore  much  more  smooth  and  pleasant  to 
travellers.  Thus  the  blacksmith  puts  his  anvil  on  a  block 
of  wood  to  lessen  the  concussion.  The  only  objection  to 
them  is  their  liability  to  decay,  against  which,  howevei, 
there  are  many  preservatives 

They  are  usually  of  chesnut,  oak,  pitch-pine,  or  red 
cedar.  They  may  be  round  slicks,  hewn  on  two  sides, 
so  as  to  leave  at  least  six  inches  thickness,  and  more  if 
possible.  The  longer  they  are  the  better,  as  the  extra 
length  on  each  side  of  the  track  lessens  the  danger  of  set- 
tling. On  the  Massachusetts  ro*ads  they  are  of  second 
growth  chesnut,  7  feet  long,  and  8  inches  by  12.  They 
are  simply  laid  on  the  ballasting,  excepl  on  new  embank 
menls  and  soft  ground  in  which  cases  ihey  are  laid  on 
longitudinal  timbers  or  sub-sills,  •which  may  be  of  plank 
8  inches  wide  and  3  or  4  thick. 


CONTINUOUS  SUPPORTS.  305 

The  "  ties,"  or  cross-sleepers,  can  be  made  to  last  much 
longer  by  preserving  them  by  chemical  means.  Some  of 
the  methods  are  given  on  p.  254. . 

CONTINUOUS  SUPPORTS. 

When  rails  are  supported  at  intervals,  the  less  the  in- 
tervals and  the  nearer  the  supports,  the  less  will  be  the 
yielding  and  deflection  of  the  rails.  Carrying  out  this 
principle,  and  continually  lessening  the  intervals,  we  at 
last  arrive  at  continuous  supports.  The  advantages  of 
such  solid  bearings  for  the  rails  would  seem  to  admit  of 
no  dispute.  It  is  evident  that  an  iron  bar,  laid  on  a  series 
of  points,  will  be  much  more  easily  bent,  either  laterally 
or  vertically,  by  the  heavy  blows  or  jolts  of  a  carriage, 
than  when  the  same  bar  is  made  to  form  a  part  of  the 
solid  roadway.  The  system  of  continuous  supports  ol 
longitudinal  timbers  is  therefore  superior  to  any  other  in 
strength,  solidity,  and  ease  of  motion.  It  has  been  of  late 
increasing  in  popularity  in  England,  in  spite  of  the  cost 
of  .timber  in  that  country,  while  with  us  it  has  been  aban- 
doned on  our  best  roads  for  the  system  of  supports  at 
intervals.  This  has  probably  arisen  from  the  circum- 
stance that  most  American  roads  with  longitudinal  timbers 
have  been  laid  with  plate  rails,  so  thin  that  their  ends 
sometimes  spring  up  so  as  to  form  "  snake-heads,"  arid 
have  thus  received  the  scarcely  caricatured  description  of 
"  A  hoop  tacked  to  a  lath."  Such  roads  have  the  defects 
of  instability,  insecurity,  inequality  of  surface,  waste  of 
power,  resistance  to  speed,  and  great  expense  of  main- 
tenance. But  these  faults  do  not  belong  to  the  system  it- 
self, -but  to  its  imperfect  execution.  The  rails  should  be 
heavy  edge  rails,  of  suitable  form,  and  in  :ontact  with  me 
timbers  for  their  whole  length  ;  and  the  longitudinal  timbers 


30G 


RAIL-ROADS. 


should  be  tied  together  by  cross-sleepers.     The  best  rail 
road  in  the   world,  the  "  Great  Western,"  has  such  con 
tinuous  bearings.     The  wood   may  be  preserved    from 
decay  by  any  of  the  methods  noticed  on  page  234. 
Fig.  135. 

n  n       n       n       n       n 


In  the  above  figure,  A  is  the  ground  plan,  B  the  side 
view,  and  C  the  end  view,  of  such  a  system  of  railroad. 


Fig.  136. 


For  these  longitudinal 
bearings,  chairs  are  un- 
necessary, and  peculiarly 
shaped  rails  are  preferable. 
A  favorite  form  is  that 
shown  in  Fig.  136,  which 
has  been  made  to  weigh 
from  35  to  60  Ibs.  per  yard. 
It  is  fastened  by  screws,  4  inches  long,  the  heads  of  which 
are  countersunk  on  the  inner  side,  so  as  to  be  out  of  the 
way  of  the  flange  of  the  wheel.  At  the  joints,  four  screws 
are  employed. 

Sometimes  the  rails  are  fastened  by  spikes  with  bent 
heads,  driven  just  outside  of  them,  and  clasping  them 
firmly. 

The  greater  difficulty  of  packing  the  gravel   around 


CONTINUOUS    SUPPORT. 


307 


Fig.  137. 


such  longitudinal  sleepers,  and  of  removing  and  replacing 
them,  is  the  chief  cause  of  the  general  preference  of  cross- 
ties,  or  transverse  sleepers. 

Triangular  sleepers  have 
been  employed,  with  a  rail 
forked  at  bottom,  as  in  the 
figure.  The  rail  can  thus 
be  very  firmly  attached  to 
the  sleeper,  the  shape  of 
which  gives  it  much  sta- 
bility. 

Evans'  method  of  fastening  is  warmly  recommended  by 
Professor  Vignoles.  The  rails  are  rolled  with  a  slit,  or 
groove,  of  a  dove-tailed  shape,  (in  its  cross-section)  run- 
ning on  their  under  side  for  their  whole  length.  The  bolts 
have  heads  of  corresponding  shape,  and  are  slipped  into 
the  end  of  the  groove,  passed  along  it,  and  dropped  through 
holes  made  at  proper  intervals  in  the  longitudinal  timbers. 
The  lower  ends  of  the  bolts  are  cut  into  screws,  and 
washers  and  nuts  draw  the  rails  close  down  to  the  tim- 
bers. They  are  easily  tightened,  and  not  exposed  to  in 
jury,  while  spikes  and  screws  get  loose,  and  their  heads 
are  in  the  way. 

Upon  the  Great  Western  Railroad,  between  Bristol  and 
London,  (on  which  Mr.  I.  K.  Brunei  first  introduced  into 
England  the  system  of  longitudinal  bearings)  the  hollow 
rail,  shown  in  Fig.  138,  was  Fig.  138. 

adopted.  The  original  rails 
weighed  only  44  Ibs.  to  the 
yard,  and  were  1£  inch  high, 
the  head  of  the  inner  screw 
being  countersunk.  The  later  ones  weigh  70  Ibs.  to  the 
yard,  and  are  2^  inches  high  ;  the  increase  of  height  be- 


308  RAIL-ROADS. 

ing  intended  to  compensate  for  not  countersinking  the  nut 
of  the  inner  screw.  The  longitudinal  timbers  are  15  by 
9  inches,  and  the  cross-ties  bolted  to  them  at  intervals  of 
9  or  10  feet,  are  5  by  8  inches.  With  such  rails,  and  the 
broad  gauge,  this  railroad  combines  speed  and  ease  of 
motion  in  the  highest  degree  yet  attained. 

INCLINATION    OF    THE    RAILS. 

The  wheels  having  a  conical  shape,  they  would  touch 
a  level  rail  only  on  a  narrow  line,  and  both  would  soon  be 
worn  into  grooves.  To  prevent  this,  the  rails  are  some- 
times inclined  inward,  so  as  to  meet  the  cone  of  the  wheel 
more  directly,  and  to  present  a  broader  bearing  surface. 
The  usual  inclination  is  from  1  in  29  to  1  in  20.  It  may 
be  given  by  sloping  the  blocks,  or  by  cutting  the  sleepers 
which  support  the  rails,  or  may  be  formed  in  the  original 
rolling  of  the  rail.  An  objection  to  this  breadth  of  con- 
tact is  that  a  rubbing  and  grinding  action  is  constantly 
caused  by  the  unequal  velocities  with  which  the  outer  and 
inner  parts  of  the  coned  wheels  revolve,  and  produces  the 
same  effect  as  if  the  train  was  dragged  a  certain  dis- 
tance with  its  wheels  locked. 

ELEVATION    OF    OUTER    RAIL. 

When  a  railroad  car  enters  upon  a  curve,  the  centrifu- 
gal force  tends  to  force  the  flanges  of  its  wheels  against 
the  outer  rail.  To  resist  this  tendency,  the  outer  rail  is 
made  higher  than  the  inner  one,  so  that  an  inclined  plane 
may  be  formed  beneath  the  cars,  down  which  they  will 
tend  to  slide  in  an  inward  direction,  in  oppos'tion  to  their 
centrifugal  impulse.  The  inclination  should  be  such  that 
the  two  antagonist  forces  may  just  balance  each  other.  It 
will  vary  with  the  radius  of  the  curve,  the  velocity  upon 


ELEVATION     OF    OUTER    RAIL. 


309 


it,  the  gauge  of  the  road,  and  the  "  cone"  of  the  wheels 
With  these  elements  it  may  be  readily  calculated.*  Some 
results  (with  the  usual  data)  are  given  in  the  following 
table  : 


RADIUS  OF  THE 
CURVE. 

ELEVATION  OF  THE  OUTER  RAIL. 

At  10  miles  per  hour. 

At  20  miles  per  hour. 

At  30  miles  per  hour. 

Feet. 

Inches. 

Inches. 

Inches. 

250 

1.14 

5.60 

12.99 

500 

0.57 

2.83 

6.56 

1000 

0.29 

1.43 

3.30 

2000 

0.15 

0.71 

1.65 

3000 

0.10 

0.47 

1.10 

4000 

0.07 

0.36 

0.83 

5000 

0.06 

0.28 

0.66 

An  approximate  rule  for  finding  the  elevation  is  this  : 
"  Multiply  the  square  of  the  velocity,  in  feet  per  second, 
by  the  gauge  of  the  railroad  in  inches ;  and  divide  the 
product  by  the  accelerating  force  of  gravity,  multiplied 
by  the  radius  of  curvature  in  feet,  and  the  quotient  will 
be  the  elevation  in  inches." 

For  a  velocity  of  30  miles  per  hour  on  a  curve  of  1000 

feet,  this  rule  gives  ~^-~  fr  3-4  inches. 

The  old  practice  made  the  greatest  elevation  1  inch; 
which  is  that  due  to  a  velocity  of  30  miles  per  hour  on  a 
curve  of  two  thirds  of  a  mile  radius.  When  the  cars  go 
faster  than  the  velocity  assumed  in  the  calculation,  which 
has  determined  the  elevation,  their  flanges  piess  the  outer 
rail ;  when  slower,  they  press  the  inner  one, 

SIDINGS,    CROSSINGS,    ETC. 

On  railroads  which  have  only  a  single  track,  a  second 
one,  called  a  siding,  is  occasionally  laid  for  a  short  dis 


*  See  Pambour.  pp.  277-290  ;  and  Lecount,  pp.  135-140. 


310 


RAIL-ROADS. 


tance,  to  form  a  passing-place  for  meeting  trains.  Cross- 
ings are  the  arrangements  by  which  cars  pass  from  one 
track  to  the  other.  The  angle  of  their  divergence  should 
not  exceed  1 1°  or  2°  for  speeds  of  20  or  30  miles  per 
hour,  but  when  the  speed,  as  in  mines,  is  not  more  than 
8  miles  per  hour,  the  angle  may  be  as  many  degrees.* 
They  are  always  dangerous,  and  therefore  the  fewer  of 
them  that  are  employed  the  better.  The  misplacing  of 
them,  carelessly  or  malevolently,  causes  a  large  portion 
of  the  accidents  on  railways.  Their  simplest  form  is  that 
of  two  "  points"  or  "  switches,"  which  are  attached  at  one 
end  to  the  main  track,  and  are  moveable  at  the  other,  so 
as  to  continue  the  principal  line,  or  to  connect  it  at  pleas- 
Fig.  139. 


ure  with  the  side-track.  The  switches  are  usually  moved 
by  hand,  with  either  a  lever  or  an  eccentric.  A  signal 
plate  at  the  top  of  the  lever,  with  which  it  moves,  by  its 
position  shows  to  the  engine-driver,  as  he  approaches,  to 
which  track  it  is  prepared  to  turn  the  train.  Self-acting 
switches,  kept  in  place  by  powerful  spiral  springs,  and 
moved  by  the  flanges  of  the  engine  wheels,  have  been 
tried ;  but  the  system  of  manual  operation  is  preferred, 
with  all  its  uncertainties,  owing  to  the  self-acting  arrange- 
ment rendering  it  impossible  for  the  conductor  to  know 
whether  the  switches  are  in  place  or  not  until  he  is  upon 


Cresy,  Encyclopedia  of  Civil  Engineering,  p.  1576. 


TURN-TABLES,    £1C.  Sll 

them,  when  any  precaution  which  might  be  required 
would  be  too  late.* 

Turn-tables,  or  Turn-plates,  are  platforms,  turning  on 
rollers  upon  an  underground  circular  railroad,  and  forming 
a  very  convenient  substitute  for  switches,  in  transferring 
carriages  from  one  set  of  rails  to  another. 

A  Hydraulic  Traversing  Frame  has  been  used  instead 
of  Turn-tables.  It  consists  of  a  wrought-iron  frame,  un- 
der each  corner  of  which  is  a  cast-iron  hydraulic  press, 
operated  by  force  pumps.  The  frame  is  pushed  under 
the  carriage  to  be  moved,  the  pumps  are  worked,  and 
raise  the  flanges  clear  of  the  rails.  The  carriage  is  then 
moved  to  the  desired  spot  and  there  let.  down.t 

SINGLE    RAIL    RAILROAD. 

In  this  arrangement  a  single  rail  is  supported  on  posts 
at  a  suitable  height  above  the  ground,  and  passes  through 
the  middle  of  the  cars,  which  hang  from  it  on  each  side, 
like  two  saddle-bags  on  a  horse.  The  advantages  of  thus 
lowering  the  centre  of  gravity  are  considerable  ;  the  cars 
can  never  leave  the  track  ;  and  the  expenses  of  construe 
tion  are  much  reduced.  In  some  situations  this  system 
might  be  very  conveniently  employed. 

The  engines  devised  by  Mr.  Fell  require  three  rail?,  the  centre  one  being 
gripped  by  horizontal  driving  wheels.  This  system  not  only  gives  great  in- 
crease of  tractive  power,  but  is  much  safer,  the  central  rail  making  it  almost 
impossible  for  the  engine  to  leave  the  track.  It  was  used  for  the  railroad  over 
Mount  Cenia. 


»  Ritchie,  p.  115. 

t  Cresy,  Encyclopedia  of  Civil  Engineering,  p.  1888. 


312 


RAIu-ROADS. 


IV.  MOTIVE  POWERS. 

The  principal  powers  which  have  been  employed  to 
move  carriages  on  railroads  are  Horses,  Stationary  En- 
gines, Locomotives,  and  Atmospheric  Pressure. 

X.  HORSE  POWER. 

The  power  of  a  horse  in  moving  heavy  loads  at  a  slow 
rate,  has  been  given  on  page  67 ;  the  usual  conventional 
assumption  being  150  Ibs.  moved  at  the  rate  of  2^  miles 
per  hour  for  8  hours  a  day.  At  greater  speeds  his  power 
very  rapidly  diminishes,  a  large  portion  of  it  being  ex- 
pended in  moving  liis  own  weight.  The  following  table 
shows  the  results  obtained  by  different  authors  ;  those  of 
Tredgold  being  for  6  hours  daily  labor,  and  those  of  Wood 
for  10  hours. 


VELOCITY. 

FORCE    OF    DRAUGHT  J    ACCORDING    TO 

Miles  per  hour. 

Leslie. 

Tredgold. 

Wood 

2 

100 

166 

125 

3 

81 

125 

83 

4 

64 

83 

62 

5 

49 

42 

50 

6 

36 

42 

7 

25 

36 

8 

16 

31 

10 

4 

25 

11 

1 

23 

12 

0 

21 

From  the  above  table  it  appears  that,  according  to  Wood, 
at  4  miles  per  hour  a  horse  can  draw  only  half  his  load 
at  2  miles  ;  at  8  miles  only  a  quarter  ;  and  so  on. 

At  10  miles  per  hour  Tredgold  considers  the  power  of 


MOTIVE    POWERS.  313 

a  horse  to  be  37  Ibs.  moved  10  miles  per  day.  At  the 
same  velocity  Sir  John  Macneill  estimates  it  at  60  Ibs., 
moved  8  miles  per  day. 

The  power  of  a  horse  is  also  very  rapidly  diminished 
upon  an  ascent.  On  a  slope  of  1  in  7  (8y°)  he  can  carry 
up  only  his  own  weight,  without  any  load. 

It  is  consequently  very  desirable  to  find  a  motive  power 
on  railroads,  so  much  of  which  would  not  be  uselessly 
lost  at  the  high  speeds  which  their  diminution  of  friction 
renders  possible.  Steam  has  been  therefore  employed, 
through  the  medium  of  Stationary  Engines,  and  of  Loco- 
motives. 

2.   STATIONARY  ENGINES, 

Stationary  steam  engines  were  once  the  rivals  of  loco- 
motives, as  motive  powers  for  railroads,  and  were  recom- 
mended by  two  distinguished  engineers,  less  than  twenty 
years  ago,  for  adoption  on  the  Liverpool  and  Manchester 
railway.  It  was  proposed  to  place  fixed  engines  along  the 
line,  at  stations  1|  miles  apart.  These  engines  were  to 
turn  large  drums,  or  cylinders,  around  which  were  wound 
ropes,  4  or  5  inches  in  diameter,  stretched  along  the  road 
between  the  rails,  and  supported  on  rollers.  The  wagons 
were  to  be  hooked  to  the  ropes,  and  would  be  drawn  on- 
wards with  them,  as  they  were  wound  up  on  the  revolving 
cylinders.  An  endless  rope  might  also  be  employed,  and 
two  trains  of  cars  be  drawn  at  the  same  time  in  opposite 
Fig.  140. 


directions,  as  indicated  by  the  arrows  in  the  figure.    When 
»he  cars  had  passed  over  the  mile  and  a  half,  and  reached 


314  RAIL-ROADS. 

the  end  of  one  rope,  they  could  be  detached  from  it,  and 
attached  to  the  succeeding  one,  without  any  stoppage. 

The  system  has  some  advantages  for  short  lines  over 
which  the  travel  must  pass  at  brief  intervals,  owing  to  the 
economy  of  working  stationary  engines  ;  but  it  is  utterly 
unsuiled  for  general  use.  Its  radical  defect  is,  that  the 
disarrangement  of  any  single  length  of  it,  by  any  acci- 
dent, must  stop  the  travel  on  the  whole  line.  It  is  a  chain, 
the  failure  of  any  link  of  which  will  render  the  whole  use- 
less. It  is  therefore  now  seldom  employed,  except  on 
inclined  planes. 

A  very  convenient  application  of  the  system  is,  how 
ever,  seen  on  the  London  and  Blackwall  railway,  3£  miles 
long,  with  a  fixed  engine  at  each  end.  In  this  short  dis- 
tance there  are  five  intermediate  stations  ;  but  no  deten 
lion  is  caused  by  them,  for  a  car  is  appropriated  to  each 
in  propei  order — the  last  of  the  train  being  the  one  be 
longing  to  the  first  station,  and  so  on.  On  reaching  it,  the 
soit  of  pincers  by  which  the  car  is  attached  to  the  rope,  is 
opened,  and  the  car  there  stops,  while  the  others  of  the 
train  move  on. 

A  railroad  worked  by  a  stationary  engine,  would  be  the 
most  convenient  method  of  relieving  the  rush  of  travel 
through  Broadway.  The  railroad  track  should  be  sup- 
ported on  iron  columns,  out  of  the  way  of  carriages,  as  in 
the  figure.  These  columns  might  be  placed  on  the  edges 
of  the  sidewalks,  where  now  are  the  lamp  and  awning 
posts,  and  by  extending  over  the  gutter  they  would  have  a 
base  of  3  feet.*  Their  lower  extremities  should  be  set 

*  This  arrangement  of  the  columns  was  suggested  by  Charles  Ellett, 
Jim.,  C.  E.,  in  1844,  for  an  "  Atmospheric  Railroad."  In  1834,  Mr.  J.  H. 
Patten  proposed  to  use  a  secondary  street,  and  to  connect  the  columns  by 
arches  across  the  street,  forming  a  flooring  on  which  horses  should  travel 


STATIONARY    ENGINES. 

Fig.  141 
BROADWAY    RAILROAD. 


in  heavy  masses  of  masonry.  At  top  they  should  spread 
outward,  a  foot  on  each  side,  which  would  give  sufficient 
width  for  the  railroad  track.  The  columns  should  be  set 
at  distances  of  15  or  20  feet,  and  connected  by  flat  arches. 
There  would  be  no  flooring  over  the  street,  and  the  rails 
would  intercept  no  more  light  than  do  the  boards  which 
now  connect  the  awning  posts.  No  locomotives,  or  even 
horses,  would  pass  over  the  road  ;  but  an  endless  rope 
would  continually  run  over  pulleys,  and  light  cars  would 
be  under  the  most  perfect  control,  and  could  be  attached 
to  it,  or  disengaged,  at  will,  and  stopped  more  easily  than 
an  ordinary  omnibus.  At  the  upper  end  of  Broadway,  a 
stationary  engine,  or  the  water-power  of  the  Croton,  would 
easily  and  cheaply  keep  up  the -circulation,  which  would 
pass  up  one  side  of  the  street  and  down  the  other.  At 
each  corner  might  be  a  platform,  to  which  there  would  be 
a  short  flight  of  steps  from  the  sidewalk,  the  asceril  of 
which  would  be  very  easy  ;  or  a  certain  number  of  corner 
houses  might  be  used  as  depots,  so  that  passengers  might 
step  into  the  cars  from  their  second-story  windows.  As 


316  RAIL-ROADS. 

• 

these  cars  would  replace  the  omnibuses,  the  entire  street 
would  be  left  for  miscellaneous  travel. 

A  railroad  on  the  surface  of  the  ground,  with  its  con- 
tinual stream  of  cars  stopping  up  the  cross-streets  every 
minute,  would  create  a  worse  evil  than  that  which  it  was 
intended  to  remedy  ;  and  the  endless  rope  could  not  be 
applied  to  it.  If  a  railroad  were  made  through  a  sec- 
ondary street,  passengers  would  not  generally  leave  Broad- 
way to  avail  themselves  of  it.  A  surface  railroad  being 
thus  out  of  the  question,  two  alternatives  remain.  The 
underground  one  will  find  few  advocates  ;  and  the  only 
feasible  arrangement  seems  to  be  the  column  and  endless 
rope  system.  With  its  cheap  construction,  economical 
working,  and  thronged  travel,  it  could  scarcely  fail  to  be 
the  most  profitable  railroad  ever  built,  and  might  be  made 
to  add  largely  to  the  city  revenue. 

3.  LOCOMOTIVE  ENGINES. 

When  a  steam  engine  is  required  to  move  from  its 
place,  and  to  travel  with  its  load,  as  do  horses  of  flesh  and 
blood,  its  usual  weighty  appendages  of  cold-water  cistern, 
walking-beam,  fly-wheel,  &c.,  must  be  dispensed  with. 
High-pressure  sleam  must  therefore  be  employed  in  order 
to  enable  the  engine  to  combine  the  necessary  compact- 
ness, lightness,  and  powei 


The  first  locomotive  engine  was  constructed  in  1802, 
by  Richard  Trevithick,  who  took  out  a  patent  in  conjunc 
tion  with  Andrew  Vivian.*  Both  were  Cornwall  engi 


•In  1759,  however,  Dr.  Robison,  then  a  student  in  the  University  of 
Glasgow,  suggested  to  Wa     tho  application  of  the  steam  engine  to  moving 


LOCOMOTIVE    ENGINES.  317 

neers.  This  engine  was  tried  on  common  roads,  but  in 
1 804,  Trevithick  applied  a  second  one  to  a  tram-road  in 
South  Wales,  on  which  it  drew  ten  tons  of  iron  at  the 
rate  of  5  miles  an  hour. 

Many  years  elapsed  before  any  considerable  improve- 
ments were  made,  owing  in  a  great  degree  to  useless 
efforts  to  overcome  a  difficulty  which  never  had  any  real 
existence.  When  steam  is  applied  to  propel  a  wheel 
carriage,  each  piston-rod,  to  which  the  steam  gives  a  back- 
ward and  forward  motion,  is  attached  to  a  pin  on  one  of 
the  wheels,  called  the  driving-wheel,  and  turns  it  by  a 
crank,  as  a  man  turns  a  grindstone.  If  there  was  no 
friction  between  the  wheel  and  the  road,  the  -wheel  would 
turn  around,  while  the  carriage  would  remain  stationary 
But  the  friction,  which  does  exist,  prevents  the  wheel 
from  slipping,  and  it  is  enabled  to  turn  only  by  propelling 
the  carriage  forward  over  a  distance  equal  to  the  circum- 
ference of  the  wheel  for  each  complete  revolution  of  it. 
The  imaginary  difficulty  referred  to,  was  the  notion  that 
the  adhesion  or  "  bile"  between  the  wheel  and  the  rail, 
was  so  slight  that  with  a  load,  and  particularly  on  an  as- 
cent, the  wheels  would  slip,  slide,  or  "  skid,"  either  com- 
pletely or  partially,  and  thus  fail  to  propel  the  engine. 

Great  ingenuity  was  expended  in  devising  remedies  for 
this  non-existent  evil.  Wheels  were  at  first  made  with 
knobs  and  claws  to  take  hold  of  the  ground  ;  in  1811  a 
toothed  rack  was  laid  along  the  road,  and  a  wheel  with 
teeth  was  attached  to  the  engine  and  fitted  into  the  rack  ; 

wheel  carriages.  la  1782,  Murdoch,  to  whom  Trevithick  was  a  pupil, 
made  a  model  of  a  steam-carriage  ;  and  in  1784  Watt  described  such  an 
application  in  his  patent  In  1801,  Oliver  Evans  in  Philadelphia  moved  a 
^team-dredging  machine  a  mile  and  a  half  on  wheels  turned  by  its  owu 
engine. 


318 


RAIL-ROADS. 


and  in  1812  a  chain  was  stretched  between  the  extreme 
ends  of  the  road,  and  passed  around  a  grooved  wheel  fixed 
to  the  engine  and  turned  by  it.  But  the  most  singulai 
and  ingenious  contrivance  was  patented  in  1813  by  Mr. 
William  Brunton.  He  attached  to  the  back  of  his  engine 
two  legs,  or  propellers,  which,  being  alternately  moved  by 
the  engine,  pushed  it  before  them.  The  propellers  imita- 
ted the  legs  of  a  man,  or  the  fore  legs  of  a  horse,  as  shown 
in  the  figure. 

Fig.  142. 


The  legs  are  indicated  by  HKF,  and  Ukf.  H  repre- 
sents the  Hip-joint,  K  and  k  the  Knee-joints,  A  and  a  the 
Ankle-joints,  and  F  and /the  Feel. 

We  will  first  examine  the  action  of  the  front  leg.  The 
knee,  K,  is  attached  to  the  end  of  the  piston-rod,  which 
the  steam  drives  backward  and  forward  in  the  horizontal 
cylinder  C.  When  the  piston  is  driven  outward,  it 
presses  the  leg,  KF,  against  the  ground,  and  thus  propels 
the  engine  forward  as  a  man  shoves  a  boat  ahead  by 
pressing  with  a  pole  against  the  bottom  of  a  river.  As 
the  engine  advances,  the  leg  straightens  the  point  II  is 


LOCOMOTIVE    ENGINES  319 

carried  forward  and  the  extremity,  M,  of  the  bent  lever, 
HM,  is  raised.  A  cord,  MS,  being  attached  to  S.  the 
shin  of  the  leg,  the  motion  of  the  lever  tightens  the  cord, 
and  finally  raises  the  foot  from  the  ground  and  prepares  it 
to  take  a  fresh  step  when  the  reversed  action  of  the  piston 
has  lowered  it  again. 

The  action  of  the  other  leg  is  precisely  similar,  but 
motion  is  communicated  to  it  from  the  first  one.  Just 
above  the  knee  of  the  front  leg,  at  N,  is  attached  a  rod. 
on  which  is  a  toothed  rack,  R.  Working  in  it  is  a  cog- 
wheel, which  enters  also  a  second  rack,  r,  below  it, 
which  is  connected  by  a  second  rod,  with  a  point,  n,  of  the 
other  leg.  When  the  piston  is  driven  out  and  pushes  the 
engine  from  the  knee,  the  rack,  R,  is  drawn  backwards 
and  turns  the  cog-wheel,  which  then  draws  the  lower  rack, 
r,  forwards,  and  operates  on  the  hind  leg,  precisely  as 
the  piston-rod  does  on  the  front  one,  and  thus  the  two  legs 
take  alternate  steps,  and  walk  on  with  the  engine. 

This  locomotive,  or  "  mechanical  traveller,"  as  it  was 
termed  by  its  inventor,  moved  on  a  railway  at  the  rate 
of  2^  miles  per  hour,  with  the  tractive  force  of  4 
horses. 

All  these  contrivances  were,  however,  rendered  useless 
by  the  discovery  in  1814,  by  actual  experiment,  that  the 
adhesion,  or  friction,  of  the  wheels  was  amply  sufficient 
for  propelling  the  engine,  even  with  a  heavy  load  attached 
to  it,  and  up  a  considerable  ascent.  Even  if  the  adhesion 
were  less  than  it  is,  it  could  be  increased  to  an  almost  un- 
limited extent,  by  inducing  a  galvanic  action  between  the 
engine  and  the  rails.* 

The  first  really  successful  locomotive  was  constructed 


*  Lecotmt,  p.  352. 


320  RAIL-ROADS. 

by  Mr  George  Stephenson  in  1814.  By  applying  the 
"  steam  blast,"  he  doubled  its  power  and  enabled  it  to  run 
6  miles  oer  hour,  and  to  draw  30  tons 

Still  no  great  progress  was  made  in  the  application  of 
steam  to  locomotion,  until,  in  1829,  the  directors  of  the 
Liverpool  and  Manchester  railway  resolved  to  employ 
locomotives  in  preference  to  stationary  engines,  and  offered 
a  premium  for  the  best  engine,  not  heavier  than  six  tons, 
which  should  be  able  to  draw  twenty  tons  at  the  rate  of 
ten  miles  per  hour,  and  should  fulfil  certain  other  condi- 
tions. Four  engines  appeared,  but  the  "  Rocket"  engine, 
made  by  Mr.  Robert  Stephenson,  won  the  prize,  having 
run  at  an  average  speed  of  15  miles  per  hour,  and  hav- 
ing performed  one  mile  at  the  rate  of  29 £  miles  per 
hour.  : 

Since  that  time  the  progress  of  improvement  has  been 
onward,  and  one  engine  has  travelled  75  miles  per  hour ; 
another,*  weighing  15£  tons,  has  drawn  1268  tons 
(in  a  train  of  158  coal-cars,  2020  feet  long)  84  miles  in  8 
hours,  over  a  line  of  which  40  miles  were  level,  and  which 
had  curves  of  only  700  feet  radius  ;  and  a  third,*  weigh- 
ing only  8  tons,  has  drawn  309  tons  on  a  level,  and  16 
tons  up  an  inclined  plane  which  rose  369  feet  to  the  mile. 
The  Rocket,  however,  contained  the  gerrns  of  all  the  prin- 
ciples which  have  been  so  wonderfully  developed  in  its 
successors,  and  which  will  now  be  briefly  noticed. 

»  Made  by  WR'am  Norris:  Philadelphia. 


LOCOMOTIVE    ENGINES.  321 


PRINCIPLES. 


iC  po\\  er  of  an  engine  is  proportional  to  the  quantity 
of  steam  which  it  can  generate  in  a  given  time  ;  for  each 
revolution  of  the  wheels  corresponds  to  a  double  stroke 
of  each  piston,  and  consequently  to  four  cylinder-fulls  of 
steam.  It  is  therefore  necessary  to  expose  the  largest 
possible  surface  of  water  to  the  action  of  heat.  This 
is  most  effectually  attained  by  a  tubular  boiler,  patented 
by  Mr.  Seguin  in  1828,  but  perfected  by  Mr.  Stephenson 
in  i  829.  Through  the  boiler,  which  occupies  the  principal 
mass  of  the  engine,  run  a  great  number  of  small  brass 
tubes,  and  through  them  the  flame  and  heated  air  pass 
from  the  fire-box  to  the  chimney.  The  tubes  are  about 
6  feet  long,  2  inches  in  diameter,  and  from  90  to  1 20  in 
number.  They  have  been  made  300  in  number,  and  \\ 
inches  in  diameter.*  By  this  contrivance,  and  by  sur- 
rounding the  fire-box  with  a  double  casing,  containing 
water,  all  the  heat  is  absorbed  by  the  water  before  it 
reaches  the  chimney. 

The  introduction  of  such  tubes  tripled  the  evaporating 
power  of  the  engine,  and  caused  a  saving  of  40  per  cent 
of  the  fuel.  But  the  abstraction  of  all  the  heat  from  the 
air,  destroyed  the  draught  of  the  chimney,  and  therefore 
the  activity  of  the  fire.  This  evil  seemed  insurmountable, 
in  spite  of  the  use  of  fanners,  till  George  Stephenson 
used  the  waste  steam,  which  passed  from  the  cylinder 
after  working  the  engine,  to  create  an  artificial  draught, 
by  discharging  it  into  the  chimney.  This  steam  blast 
has  been  termed  the  life-blood  of  the  locomotive  machine. 

To  economize  heat  still  farther,  the  cylinders  are  some- 

*  The  tubes  being  very  perishable,  the  Earl  of  Dundonald  and  others 
have  proposed  to  construct  boilers  with  the  water  in  the  tubes  to  be  heated, 
instead  of  the  fire  in  the  tubes. 


822  RAIL-ROADS. 

times  placed  within  the  smoke-box,  or  bottom  of  the 
chimney,  so  that  none  of  their  steam  is  condensed  by  the 
cold  atmosphere.  In  this  position,  besides  being  nearei 
the  centre  of  resistance,  they  act  with  a  less  injurious 
strain  ;  although,  two  pistons  being  necessary  to  pass  the 
"  dead-points"  of  the  crank,  their  action  is  unavoidably 
unequal  on  each  side  in  turn.  But  this  arrangement  gives 
less  room  for  the  machinery,  and  renders  necessary  a 
double-cranked  axle,  which  is  consequently  much  weak- 
ened, though  cut  from  a  solid  mass  of  iron.  Both 
the  outside  and  inside  arrangements  have  their  advocates. 

Six  wheels  are  generally  employed,  the  two  largest 
being  the  driving-wheels  to  which  the  power  is  applied. 
These  are  from  5  to  7  feet  in  diameter,  the  others  being 
from  3  to  4.  Sometimes  all  are  made  of  the  same  size. 
Eight  wheels  are  also  used,  four  large  and  four  small,  the 
latter  being  under  a  truck,  which  supports  one  end  of  the 
engine,  and  is  attached  to  it  by  a  pivot  in  its  centre, 
around  which  it  can  readily  turn  when  on  a  curve. 
The  springs  are  so  adjusted  that  the  principal  part  of  the 
weight  of  the  engine  is  thrown  upon  the  driving-wheels. 
Sometimes  two  pairs  of  wheels  are  coupled  together  to 
obtain  greater  adhesion  in  ascending  inclined  planes,  but 
this  arrangement  produces  an  unequal  strain. 

The  eccentrics  which  open  and  shut  the  slide-valves  to 
admit  the  steam  to  each  end  of  the  cylinders  in  turn,  are 
so  adjusted  as  to  shut  off  the  steam  from  one  end  of  the 
cylinder  and  admit  it  to  the  othe  •  a  little  while  before  the 
piston  has  finished  its  stroke,  so  as  to  permit  the  expan- 
sive action  of  steam,  and  to  form  a  sort  of  steam  spring, 
lo  deaden  the  jerks  of  the  engine.  The  degree  of  open- 
ing of -the  valve  in  advance  is  termed  the  "lead,"  and 
is  usually  from  one-eighth  to  one-fourth  of  an  inch. 


LOCOMOTIVE    ENGINES. 
Fig.  143 


323 


The  above  figure  is  a  longitudinal  section  through  a 
modern  locomotive  engine,  in  one  of  its  very  varied  forms, 
a  represents  the  fire-box ;  from  which  the  flames  and 
heated  air  pass,  through  the  tubes  b  b,  into  the  smoke-box 
at  the  other  end  of  the  engine.  The  water  of  the  boiler, 
(which  is  cased  with  wood  to  prevent  loss  of  heat  by  ra- 
diation) surrounds  the  fire-box  arid  the  tubes,  and  the- 
stcarn  generated  by  the  heat  thus  absorbed,  is  collected  in 
the  steam  chamber  c.  Thence  it  passes,  through  d,  to  the 
cylinder  e,  and  being  admitted,  by  the  slide-valve,  alter- 
nately before  and  behind  the  piston,  it  gives  to  it  the  re- 
ciprocating motion,  which  the  crank  on  the  axle  of  the 
driving-wheel  converts  into  the  revolution  which  propels 
the  engine.  The  blast-pipe,/,  conveys  the  waste  steam 
from  the  cylinders  into  the  chimney,  to  increase  its 
draught,  g  g  are  safety-valves,  one  of  which  should  be 
locked  up,  so  as  to  be  out  of  the  control  of  the  engine- 
driver,  h  is  one  of  the  feed-pipes  which  conduct  the 
water  from  the  tender  to  the  boiler,  into  which  it  is 


324  RAIL-ROAOS. 

pumped  by  small  force-pumps,  which  are  worked  by  the 
engine,  and  the  derangement  of  which  has  produced  se- 
rious accidents. 

SPEED    AND    POWER. 

The  speed  of  an  engine  depends  on  the  rapidity  with 
which  its  boiler  can  generate  steam.  One  cylinder  full 
of  steam  is  required  for  each  stroke  of  each  of  the  pis- 
tons. Each  double  stroke  corresponds  to  one  revolution 
of  the  driving-wheels,  and  to  the  propulsion  of  the  engine 
through  a  space  equal  to  their  circumference.  Wheels 
seven  feet  in  diameter  pass  over  twenty-two  feet  in  each 
complete  revolution.  To  produce  a  speed  of  seventy-five 
miles  per  hour,  they  must  revolve  exactly  five  times  in  a 
second  ;  and  to  effect  this  number  of  revolutions  each 
piston  must  make  double  that  number  of  strokes  in  the 
same  time.  In  this  way  does  this  ponderous  machine 
divide  time  into  tenths  of  seconds,  almost  as  precisely  as 
the  delicate  chronometer  of  the  astronomer. 

This  rapid  reciprocating  motion  of  the  pistons  is  very 
•  destructive  to  the  machinery,  and  is  too  great  to  attain  the 
maximum  effect  of  the  power  expended.  It  would  there- 
fore be  very  desirable  to  lessen  this  rapidity,  and  to  pro- 
vide some  means  of  multiplying  the  motion  of  the  pistons, 
as  by  chains  on  pulleys,  &c. 

High  velocities  are  also  very  expensive,  in  consequence 
of  the  rapidity  with  which  the  steam  must  be  generated, 
and  rammed,  as  it  were,  into  the  cylinders.  The  same 
effect  might  be  produced  by  one  quarter  of  the  quantity 
of  steam,  if  time  were  given  it  to  act  expansively. 

The  power  of  an  engine  in  drawing  loads,  depends  on 
the  pressure  of  the  steam,  which  is  usually  between  80 
and  120  Ibs.  to  the  square  inch  It  is  also  limited  by 


LOCOMOTIVE    ENGINES. 


325 


Hie  adhesion  between  the  road  and  the  driving-wheels, 
which  is  proportional  to  the  weight  pressing  upon  the 
latter ;  so  that  instead  of  the  weight  of  the  engine  being 
an  obstacle,  it  is  one  of  the  principal  elements  of  power. 
The  average  adhesion  may  be  considered  to  be  ith  the 
weight.  The  tractive  power  of  an  engine  of  20  gross 
tons  weight,  with  16  tons  resting  on  the  driving-wheels, 
would,  on  this  assumption,  be  16  x  2240  -r-  8  =4480  Ibs. 
Jf  the  friction  be  10  Ibs.  to  the  ton,  its  gross  load,  exclu- 
sive of  its  own  weight,  would  be  4480  -r-  10  =  448  tons. 
If  the  ratio  of  the  weight  of  the  freight  to  the  joint  weight 
of  the  car  and  freight  be  as  6  to  10,  the  quantity  of  freight 
which  such  an  engine  could  convey  on  a  level  would  be 
T^  X  (448—10)  =  263  tons;  the  weight  of  the  tender, 
10  tons,  being  deducted  from  the  gross  load. 

The  diminution  of  this  power  on  inclinations  has  been 
noticed  on  page  276,  but  is  more  fully  shown  in  the  fol- 
lowing Table,  which  is  calculated  for  an  engine  of  20  tons, 
all  resting  on  the  driving-wheels,  and  for  a  friction  of  8^ 
Ibs.  to  the  ton. 


Ascent,  in 
feet  per  mile. 

Tons  of  freight 
transported. 

Fractional  part 
of  the  full  load 
on  a  level. 

Number  of  engines 
necessary  to  trans- 
port the  full  load. 

Level. 

389 

1.000 

r 

10 

254 

.653 

If 

20 

185 

.476 

2r 

30 

145 

.372 

2| 

40 

118 

.304 

3J 

50 

98 

.252 

4 

60 

84 

.215 

4| 

70 

71 

.180 

6f 

80 

63 

.160 

e| 

326 


RAIL-ROADS. 


The  friction  of  8}  Ibs.  to  the  ton,  with  which  the  pre- 
ceding table  was  calculated,  was  found  (p.  265)  to  be  too 
small.  The  following  table  has  been  calculated  by  taking 
the  friction  at  10  Ibs.  per  ton,  (the  average  amount  for  a 
slow  freight  speed,)  the  other  data  remaining  unchanged. 
The  principles  of  the  calculation  are  found  on  pages  325 
and  276-7.  The  adhesion  is  taken  at  one-eighth  of  the 
weight  resting  on  the  driving  wheels.* 


Ascent,  in 
feet  per  mile. 

Tons  of  freight 
transported. 

Fractional  part 
of  the  full  load 
on  a  level. 

Number  of  engines 
necessary  to  trans- 
port the  full  load. 

Level. 

330 

1.000 

1 

10 

227 

.688 

14 

20 

170 

.515 

2 

30 

135 

.401 

2* 

40 

111 

.333 

3 

50 

94 

.284 

n 

00 

80 

.242 

4 

70 

70 

.211 

4} 

80 

61 

.185 

5 

The  above  table  shows  that,  with  its  data,  on  an  asceiu 
of  20  feet  per  mile,  two  engines  will  be  required  to  trans- 
port the  load  which  one  could  draw  on  a  level ;  that  three 
engines  would  be  required  on  an  ascent  of  40  feet  per 
mile,  and  so  on. 

A  comparison  of  the  two  tables  also  shows  that  by  assuming 
a  small  amount  of  friction,  ascents  are  made  to  appear  much  more 
objectipnable,  relatively,  than  if  a  larger  amount  of  friction  had 
been  employed.  Thus,  on  an  ascent  of  50  feet  per  mile,  accord- 
ing to  the  former  table,  (calculated  with  the  insufficient,  though 
commonly  assumed  friction  of  8^  Ibs.  to  the  ton,)  four  engines 
are  required  to  do  the  work  of  one  upon  a  level ;  but  the  latter  and 
more  correct  table  shows  that  only  three  and  a  half  are  needed. 
For  higher  speeds,  and  consequently  greater  resistances,  the  same 
ascents  would  be  found  to  be  relatively  much  less  injurious, as  has 
been  shown,  on  page  34,  with  reference  to  common  roads. 

*  The  greatest  adhe8ion  of  iron  upon  iron  is  about  one-sixth  of  tne  insist* 
ent  weight ;  but  in  wet  and  freezing  weather  becomes  almost  nothing.  It 
lessens  with  the  increase  of  the  slope  of  the  road,  nearly  as  the  sine  of  the  an- 
gle of  inclination.  It  would  evidently  be  nothing,  if  the  road  werp  vpHi«vi. 


WORKING     EXPENSES.  321 


WORKING    EXPENSES. 

All  the  expenses  of  working  the  road  for  any  given  time 
are  usually  added  together,  and  divided  by  the  total  num- 
ber of  miles  run  in  that  time  by  engines  drawing  trains. 
In  this  way  is  obtained  the  common  average  of  working 
expenses,  which  are  thus  measured  by  the  cost  of  running 
trains  per  mile.  But  this  principle  of  comparison  is  evi- 
dently faulty,  since  a  train  may  be  run  for  a  very  small 
cost  per  mile,  but  carry  few  passengers  and  little  freight ; 
and  thus  its  expenses,  though  small  absolutely,  may  be 
ruinously  great  relatively.  On  the  other  hand,  a  heavy 
train  may  cost  much  more  per  mile,  but  carry  so  great  an 
amount  of  freight  or  passengers,  as  to  be  run  very  cheap- 
ly, relatively  to  them.  Fifty  tons,  carried  for  75  cents 
per  mile,  would  cost  1|  cents  per  ton,  while  a  hundred 
tons  carried  for  even  $1  per  mile,  would  cost  but  1  cent 
per  ton. 

The  cost  of  transport  per  mile  for  each  passenger  or  Ion 
of  freight  carried,  is  therefore  a  preferable  standard,  with 
certain  restrictions,  as  affording  a  means  of  direct  com- 
parison between  the  expenses  and  the  receipts,  which  are 
the  final  objects  of  all  the  operations.  But  this,  again,  does 
not  of  itself  show  the  comparative  economy  of  the  working 
of  different  roads,  for  a  road  may  be  worked  very  cheaply 
per  mile  run,  but,  having  little  business,  at  a  great  cost  pei 
passenger  or  per  ton,  since  a  large  part  of  the  expenses 
a:e  the  same  for  one  passenger  or  for  a  hundred.  The  con 
verse  of  this  takes  place  on  a  heavy  road,  worked  expen- 
sively per  mile,  but  cheaply  per  passenger  or  ton  of  freight. 

Both  these  methods  of  comparison  ought,  therefore,  tc 
be  employed  in  conjunction. 


32S* 


RAIL-ROADS. 


The  complete  average  expense  per  train  per  mile  of  run- 
ning eleven  NEW  YORK  railroads  during  1850,  was  67 
cents  for  passenger  trains,  (ranging  from  34  to  94  cents,) 
jnd  87  cents  for  freight  trains,  (ranging  from  37  to  159 
cents  ;)  including  in  this  the  expenses  of  maintaining  the 
road,  of  repairing  machinery,  and  of  operating  the  road. 

Upon  the  same  roads,  the  average  cost  per  passenger 
per  mile  was  1  ffc  cents  ;  the  lowest  being  TW,  and  the 
highest  2TW-  The  average  cost  of  freight  per  ton  was 
3iVo  cents  ;  the  lowest  being  lTVo>  a°d  the  highest  4TYo 
cents.* 

Upon  five  leading  MASSACHUSETTS  Railroads,  the  aver- 
age expenses,  for  Passenger  trains,  per  mile  run,  was  74 
cents,  (from  63  to  93  cents,)  and  per  passenger  per  mile 
1  cent,  (from  TV-0  to  !TyT.) 

Upon  the  same  five  roads,  the  Freight  expenses,  per 
mile  run,  averaged  89  cents,  (from  81  to  96  cents,)  and 
per  ton  per  mile  1T%\  cents,  (from  ^°o  to  ijW) 

The  expenses  on  the  Utica  and  Schenectady  road  are 
classified  thus  :* 


Utica  and  Schenectady  Railroad. 

Passengers 
per  mile  run. 

Freight 
per  mile  run. 

1.  Maintaining  road  

22 

22 

(Repairs  and  depreciation,  taxes,  fee.) 
S.  Repairs  oj  machinery  

(Engines,  cars,  tools,  &c.) 

21 
33 

28 
94 

(Office  expenses,  Laborers,  Conductors, 
Enginemen,  &c.,  Fuel,  Oil,  and  Waste, 
Damages,    Superintendence,    Contin- 
gencies.) 

70 

143 

*  N.  Y.  State  Engineer's  Report  on  Railroad  Statistics,  Jan.  7, 1651. 


\VOKKING    EXPENSES. 


329* 


Upon  the  Eastern  Railroad  (Boston  to  Portsmouth,  54 
miles)  the  expenses  were  thus  classified  for  the  year  end- 
ing June  30,  1850:  1,037,000  passengers,  arid  71,000 
ions  of  freight  having  been  carried  :* 


EasMTn  Railroad. 

Per  mile  run. 

Per  cant. 

Machine  shop  
Maintenance  of  way  .  .  . 
Locomotive  power.  .  .. 

0.3 
12.5 
22.9 
9  9 

20 
37 
16 

Office  experses  
Station  do  
Mail  

6.0 
8.3 
0.3 

10 
13 

Ferry 

2  3 

4 

62.5 

100 

With  careful  management  in  every  department,  trains 
carrying  average  loads  of  from  100  to  150  tons  can  be 
moved,  on  ordinary  grades,  at  a  cost  of  80  cents  per  mile. 
Such  economy  of  transport  depends  mainly,  however, 
upon  the  certainty  of  always  carrying  full  loads.  For  this 
reason  the  Baltimore  and  Ohio  Railroad  carried  coal,  by 
contract,  for  1^  cents  per  ton,  while  their  ordinary  traffic, 
giving  the  engines  only  half  a  load,  cost  them  over  2|  cents. 
The  Reading  Railroad  is  said  to  be  able  to  carry  coal  for 
6  mills  per  ton  per  mile,  because  fully  loaded  on  the  down 
trips. 

The  present  cost  of  transport  on  the  Erie  Canal  is  1  r5/^ 
cents  per  ton  per  mile,  of  which  the  State  receives  T7o  cent, 
or  nearly  one-half.  On  the  Enlarged  Canal,  the  cost  is 
estimated  at  7  mills,  3  of  these  being  tolls. f 


•  Report  of  the  President,  D.  A.  Neal. 

t  N.  Y.  State  Engineer's  Report  on  Canala,  Feb.  7, 1851. 


328  RAIL-ROADS. 


SAFETY    OF    TRAVELLING. 


The  comparative  safety  of  railroads  is  one  of  their 
most  valuable  attributes,  though  the  one  least  appreciated 
and  most  imperfectly  realized.  The  popular  impression 
is  generally  the  reverse  of  the  truth,  for  tn  accident  to  a 
stage-coach  is  seldom  heard  of  beyond  the  immediate 
scene  of  its  occurrence,  while  any  railroad  disaster  is 
passed  from  paper  to  paper  over  the  whole  land. 

There  are  many  reasons  why  travelling  on  railroads 
should  be  safer  than  on  common  roads.  The  former  are 
level  instead  of  hilly,  and  smooth  instead  of  uneven ;  and 
all  miscellaneous  travel  is  excluded. 

The  cars  are  safer  than  coaches,  because  their  centres 
of  gravity  are  lower ;  their  axles  are  less  exposed  to  vio- 
lent shocks,  and  therefore  are  less  subject  to  break  ;  and 
they  are  altogether  less  exposed  to  be  overturned. 

Locomotive  engines  are  safer  than  horses,  because  they 
are  not  liable  to  take  fright,  shy,  or  run  away :  and  can 
be  stopped  at.  once  by  a  brake,  tamed  down  by  opening  a 
valve,  and  backed  by  simply  moving  a  lever. 

The  statistics  of  railroads  fully  confirm  the  conclusions 
of  theory.  On  the  English  railroads,  according  to  the 
parliamentary  returns,  between  1840  and  1845,  both  in 
elusive,  more  than  120,000,000  of  passengers  were  car- 
ried, and  of  these  only  66  were  killed,  or  one  in  nearly 
two  millions ;  and  only  324  others  were  in  any  way  in- 
jured, or  one  in  nearly  four  hundred  thousand. 

On  the  Belgian  railroads,  6,609,215  persons  travelled 
between  1835  and  1839,  and  of,  these  15  were  killed  and 
16  wounded.  But  of  these,  26  were  persons  employed 
on  the  railroads,  and  only  3  passe?igers  were  killed  and  2 
wounded.  In  1842,  of  2,716,755  passengers,  only  three 


SAFETY.  329 

were  killed,  and  of  these  one  was  a  suicide,  and  the  other 
two  met  their  deaths  by  crossing  the  line. 

On  French  railroads,  212  miles  in  length,  of  1,889,718 
passengers  who  travelled  over  316,945  miles,  in  the  first 
half  of  1843,  not  one  was  either  killed  or  wounded,  and 
only  three  servants  of  the  railroad  suffered. 

Comparing  with  this  the  travelling  by  horse-coaches  in 
the  same  region,  we  find  that  in  seven  years,  from  1834 
to  1840,  74  persons  were  killed,  and  2073  wounded  ! 

But  few  as  are  the  accidents  on  railways  they  are  still 
much  more  numerous  than  they  need  be.  They  may  be 
divided  into  those  which  arise  from  mismanagement  and 
negligence,  and  those  which  are  caused  by  inherent  faults 
in  the  construction  and  working  of  the  railroad. 

To  the  former  class  belong  accidents  from  collision. 
When  two  engines  and  trains  meet  each  other,  or  when 
one  overtakes  another,  the  destructive  consequences, 
•vhich  so  often  ensue,  are  generally  due  to  the  careless 
ness  or  ignorance  of  the  conductors,  or  engine-drivers 
of  the  train  ;  and  are  finally  attributable  to  the  false  econ- 
omy of  employing  at  a  low  salary  incompetent  persons. 
The  danger  of  collision  would  also  be  much  lessened,  if 
trains  running  in  different  directions  were  confined  inva 
riably  to  one  line  of  rails. 

Many  accidents  have  arisen  from  a  slow  train  being 
overtaken  by  a  faster  one.  There  is  extreme  danger  in 
permitting  one  engine  to  follow  another,  except  at  very 
considerable  distances ;  and  a  mile  is  a  very  short  dis 
tance  when  measured  by  the  brief  time  in  which  a  loco- 
motive can  pass  over  it. 

The  practice  of  attaching  an  engine  behind  a  train  to 
assist  the  frort  one  in  the  ascent  of  a  steep  grade,  is  also 
fraught  with  danger ;  for  any  derangement  of  either  en- 


330  RAIL-ROADS. 

gine  makes  it  the  anvil  on  which  the  oilier  one  falls  like  a 
trip-hammer,  crushing  every  thing  between  them. 

The  excessive  speed  demanded  by  the  impatience  of 
the  travelling  public  diminishes  the  controlling  power,  and 
makes  the  consequences  of  any  negligence  or  malicious 
obstruction  proportionally  destructive. 

Wilful  disobedience  of  orders  on  the  part  of  engine- 
drivers  and  conductors,  (as  to  time,  turning-out  places, 
waiting  for  other  trains,  &c.)  reckless  exposure  to  possi- 
bilities of  collision,  and  insane  confidence  in  good-luck, 
are  causes  of  the  majority  of  accidents  ;  and  though  no 
faithful  superintendent  would  permit  such  men  to  have  a 
second  opportunity  for  similar  misconduct,  yet  the  disas 
trous  effects  of  even  the  first  faults  might  be  generally 
avoided  by  employing  only  men  of  undoubted  intelli- 
gence, experience,  sobriety,  and  self-control,  and  securing 
the  services  of  the  very  best  of  their  class  by  liberal  com- 
pensations. 

The  second  division  of  accidents  included  those  caused 
by  inherent  faults  in  the  construction  and  working  of  the 
railroad.  These  may  be  in  a  great  degree  guarded 
against,  by  careful  and  continual  inspection  of  the  line  of  the 
road,  and  examination  of  all  parts  of  the  engines  and  cars. 

The  explosion  of  the  locomotive  boiler  is  often  injuri 
ous,  if  not  fatal,  to  the  engine-men,  and  by  its  stoppage 
of  the  train  may  cause  a  collision  with  a  following  one. 

The  settling  of  an  embankment  may  cause  a  depres- 
sion of  one  side  of  the  road,  which  will  compel  the  en 
gine  to  run  off.  The  looseness  of  a  rail,  its  breakage, 
(when  supported  only  at  intervals)  the  misplacing  of  a 
switch,  &c.,  may  produce  a  similar  result.  The  destruc- 
tive consequences  would  be  much  lessened,  if  means  were 
provided  for  instantly  detaching  the  train  from  the  engine, 


SIGNALS.  331 

or  if  they  were  so  coupled  that  they  would  be  sepaiated 
by  any  lateral  strain. 

The  breakage  of  the  axles  of  the  engine  or  carriages 
has  caused  many  accidents  ;  but  this  danger  is  greatly 
lessened  by  the  eight  wheels  of  the  American  cars,*  and 
by  the  appendages  of  "  Safety-beams." 

The  sparks  from  the  locomotive  chimney  frequently 
communicate  fire  to  the  train,  and  have  thus,  in  one  in- 
stance, caused  great  loss  of  life,  increased  by  the  impos- 
sibility of  communicating  the  intelligence  to  the  engine- 
driver  in  time  to  arrest  the  disaster. 


Many  of  the  accidents  which  occur  with  the  locomotive 
system  might  be  prevented  by  a  uniform,  simple,  and 
complete  plan  of  signals.  Red  flags  and  lights  for  im- 
minent danger ;  green  for  caution  ;  and  white  for  safety, 
are  leading  features  in  all  the  systems.  The  signals  are 
made  by  the  policemen,  who  are,  or  should  be,  stationed 
along  the  line,  to  see  that  the  rails  are  clear,  to  communi- 
cate intelligence,  to  work  the  signals,  &c. 

The  Danger  signal  is  a  red  flag  by  day,  or  red  glass 
lamp  by  night,  waved  backwards  and  forwards.  The  en- 
gine should  be  stopped  the  moment,  this  signal  is  seen. 
Any  signal,  violently  waved,  should  also  cause  an  imme- 
diate stoppage. 

The  Caution  signal  is  a  green  flag,  or  light,  and  should 
be  obeyed  by  slackening  the  speed  of  the  engine.  When 


*  Iu  this  respect  we  are  far  in  advance  of  European  Railroads,  and  a 
writer  in  the  Westminster  Review  lately  suggested,  as  an  improvement 
of  the  highest  importance,  a  peculiar  style  of  car,  which  was  almost  pre- 
cisely identical  with  those  which  have  been  for  many  years  in  genera! 
uee  on  American  Railroads. 


332  RAIL-ROADS. 

the  green  flag  is  held  so  as  to  point  upwards,  it  indicates 
that  another  engine  is  less  than  five  minutes  in  advance 
of  the  one  to  which  the  signal  is  made.  When  held 
pointing  downwards,  it  enjoins  a  slow  rate  of  speed  as 
a  precaution  against  defects  in  the  rails  at  that  place. 

The  Safety,  or  "  All-right"  signal,  is  a  white  lamp  at 
night,  and  by  day  the  upright  position  of  the  policeman 
with  his  flags  furled. 

These  signals  are  made  by  the  policemen,  either  with 
hand  flags  and  lamps,  or  by  arms  which  are  moveable  on 
signal  posts,  and  worked  by  cords. 

In  the  absence  of  these  conveniences  the  policeman 
makes  the  signal  "  All  right,"  by  extending  his  arm  hori- 
zontally ;  the  Caution  signal  by  holding  one  arm  straight 
up ;  and  the  Danger  signal  by  holding  both  arms 
straight  up,  or  by  waving  violently  a  hat,  or  any  other 
object. 

The  Danger  signal  is  always  to  be  made  immediately 
after  any  engine  Oi  carriage  has  passed  along  the  line, 
and  is  to  be  continued  for  five  minutes ;  it  is  also  to  be 
made  whenever  there  is  any  obstruction  on  the  line,  or 
any  danger  of  it. 

The  Caution  signal  is  always  to  follow  the  Danger 
signal,  and  to  be  continued  for  five  minutes  ;  it  is  also  to  be 
made  wherever  there  is  any  reason  for  slackening  the 
speed. 

The  All-right  signal  is  to  be  made  only  when  the  signal- 
man has  satisfied  himself  that  the  line  is  clear,  unob- 
structed, and  free  from  any  suspicion  of  danger.  Every 
signal-man  should  immediately  report  to  his  nearest 
superior  officer  any  instance  of  disobedience  to  the  signals 
which  he  had  made. 

In  foggy  weather  both  day  and  night  signals  are  given  ; 


SIGNALS.  333 

and  in  addition,  when  any  emergency  requires  the  imme- 
diate and  certain  stoppage  of  any  train,  a  detonating  com- 
pound, packed  in  a  small  box,  is  fastened  to  the  rail  with 
slips  of  lead,  and  explodes  with  a  tremendous  noise  when  a 
wheel  passes  over  it,  giving  an  unmistakeable  signal  for 
instant  stoppage. 

White  and  red  lights  on  the  front  and  back  of  a  train 
at  night  should  be  so  arranged  and  combined  as  to  indi- 
cate the  direction,  speed,  &c.  of  the  train.  But  all  these 
precautions  are  finally  dependent  for  their  complete  suc- 
cess upon  the  character  of  the  persons  in  the  employ  of 
the  company. 


334  RAIL-ROADS 


4.  ATMOSPHERIC  PRESSURE. 

The  pressure  of  the  atmosphere  is  usually  assumed  to 
be  15  Ibs.  on  every  square  inch  of  surface,  and  though 
the  equality  of  this  pressure  in  all  directions  renders  it 
generally  insensible,  it  becomes  very  apparent  to  the 
senses  when  the  hand  is  held  on  one  end  of  a  cylinder 
from  the  interior  of  which  the  air  is  drawn  out  by  an 
air-pump.  It  is  this  pressure  which  is  the  motive  power 
of  the  ATMOSPHERIC  RAILWAY. 

The  first  idea  of  such  a  construction  seems  to  have 
originated  in  1805,  in  which  year  an  Englishman,  named 
Taylor,  proposed  to  employ  atmospheric  pressure  for 
sending  letters  and  parcels  from  town  to  town.  His 
plan  was  to  lay  a  long  tube,  like  a  gas  or  water  pipe,  be- 
tween the  places,  and  to  fit  into  it  an  air-tight  piston.  If 
the  air  was  pumped  out  from  one  end  of  such  a  tube,  the 
pressure  of  the  atmosphere  would  force  forward  the  pis- 
ton, and  any  thing  attached  to  it. 

In  1810,  Medhurst  propcsed  to  make  a  lube,  archway, 
or  tunnel,  large  enough  to  contain  carriages  with  passen- 
gers, to  be  propelled  in  a  similar  manner.  But  this  scheme 
was  never  put  into  practice,  for  travellers  did  not  relish 
the  idea  of  being  shot  through  a  tube,  like  pellets  in  a 
popgun. 

The  problem  was  now  to  devise  some  means  of  com 
municating  the  motion  of  a  piston,  blown  through  an  air- 
light  tube,  to  a  carriage  on  the  outside  of  this  tube. 

Medhurst,  in  1827,  proposed  to  make  the  desired  com 
mumcation  and  application  of  power,  through  a  channel, 
or  groove,  on  the  top  of  the  tube,  filled  with  water  to 
make  it  air-tight.  He  also  suggested  the  use  of  a  square 


ATMOSPHERIC    POWER. 


335 


iron  tube,  with  half  its  top  rising  and  falling  on  hinges, 
and  an  arm  coming  through  the  opening  to  connect  the 
piston  to  the  carriage. 

Vallance,  in  1824,  patented  a  variation  of  the  tunnel  of 
Medhurst. 

Pinkus,  an  American  residing  in  London,  in  1834  pro- 
posed the  use  of  a  tube  with  a  slit  in  its  top  and  a  sort  of 
rope  for  the  covering  valve. 

But  no  substantial  success  was  attained  till  Clegg,  in 
1839,  invented  his  flap  valve,  and,  in  conjunction  with 
Samuda,  developed  the  present  system.  'Fig.  144  is  a 

Fig.  144. 


cross-section  of  the  pipe,  valve,  &c.  The  pipe,  A,  is  of  cast 
iron,  and  about  eighteen  inches  in  diameter.  It  is  laid 
between  the  rails  on  which  the  carriages  are  to  run. 
Along  its  top  is  a  continuous  slit,  or  longitvdinal  opening, 
through  which  is  to  pass  obliquely  the  iron  bar,  or. 
arm,  D,  which  connects  the  piston  C,  with  the  carriage^ 
of  which  HH  is  an  axle.  The  valve  which  covers  this  slit, 
and  which  is  shown  in  cross-section  at  B  is  essentially  a 


BAIL-ROADS. 


strip  of  leather,  one  edge  of  which  is  fastened  to  one  side 
of  the  slit,  so  that  the  rest  of  it  can  rise  and  fall,  and  thus 
alternately  open  and  close  the  slit.  In-  the  figure  it  is 
represented  as  open.  To  strengthen  it,  plates  of  iron, 
each  eight  inches  long,  are  attached  to  its  upper  and  under 
sides.  The  under  ones  are  just  wide  enough  to  fit  into 
the  slit  ;  the  upper  ones  are  a  little  wider,  to  prevent  the 
valve  from  being  pressed  into  the  pipe.  On  each  side  of 
the  slit  is  a  rib,  or  projection,  cast  with  the  pipe,  and 
forming  a  sort  of  trough,  at  the  bottom  of  which  the  valve 
lies  when  shut.  This  trough  is  filled  with  a  mixture  of 
tallow  and  bees-wax,  which,  after  being  melted  and  cool- 
ed, adheres  to  the  edge  of  the  valve  and  makes  it  perfectly 
air-tight. 

Fig.  145. 


Fig.  145  is  a  longitudinal  section  of  the  pipe,  piston, 
and  leading  carriage.  The  same  letters  of  reference  are 
employed  as  in  Fig.  144. 

A  steam  engine,  at  the  end  of  a  length  of  3  miles  of  the 
pipe,  works  an  air-pump,  which  draws  out  a.  portion  of 
the  air  from  the  pipe,  A  A.  The  air  behind  the  piston, 
(shown  at  C)  being  no  longer  Dalancea  by  the  air  before 
the  piston,  presses  it  forward.  The  small  wheels,  EEE, 


ATMOSPHERIC    POWER  337 

behind  the  piston,  raise  the  edge  of  the  valve  in  order  to 
make  way  for  the  connecting  arm,  D,  which  draws  the 
carriage  (of  which  HHH  are  the  axles)  onward  with  the 
piston.  The  small  wheels,  FFF,  behind  the  arm,  lift 
up  the  valve  to  admit  the  air  more  freely  to  press  on  the 
back  of  the  piston.  The  piston  and  carriage  thus  pro- 
ceed as  long  as  there  is  a  greater  pressure  of  air  behind 
than  before  them. 

To  re-seal  the  valve,  after  the  piston  has  passed,  in 
readiness  for  being  again  exhausted,  the  second  carriage 
of  the  train  carries  under  it  a  small  steel  wheel  which 
presses  down  the  valve,  and  which  is  followed  by  a  heater, 
or  copper  tube,  five  feet  long,  and  filled  with  burning 
charcoal,  which  melts  the  composition  in  the  trough  and 
solders  down  the  edge  of  the  valve. 

To  stop  the  train  the  brake  may  be  applied  ;  or  the 
lever,  shown  at  G  in  Figs.  144  and  145,  may  open  a 
valve  in  the  piston,  and  admit  air  in  front  of  it  to  destroy 
the  vacuum,  and  consequently  the  propelling  power. 

When  the  carriage  has  reached  the  end  of  one  length 
of  3  miles,  it  passes  into  the  next  length  of  pipe  by  an 
entrance,  or  equilibrium  valve,  ingeniously  contrived  to 
permit  the  change  without  affecting  the  vacuum. 

The  power  of  this  system  depends  upon  the  size  of  the 
pipe,  and  the  perfection  of  the  vacuum  in  front  of  the  pis- 
ton. If  the  pipe  be  18  inches  in  diameter,  the  area  of  the 
piston  will  be  254  square  inches,  and  if  a  perfect  vacuum 
could  be  attained,  the  pressure  of  the  atmosphere  upon 
this  surface  would  be  254  x  15  =  3810  Ibs.  Calling  the 
friction  10  Ibs.  to  the  ton,  this  power  would  be  sufficient 
to  move  381  tons.  In  practice,  however,  the  vacuum  is 
seldom  reduced  below  8  Ibs.  to  the  square  inch,  or  half 
an  atmosphere,  there  being  an  unavoidable  leakage. 


338  RAIL-ROADS. 

The  speed  is  proportioned  to  the  rapidity  with  which 
the  air-pump  exhausts  the  pipe,  and  therefore  to  the  ve 
locity  with  which  the  air-pump  piston  moves,  and  to  the 
ratio  between  its  area  and  that  of  the  travelling  piston. 
Air  rushes  into  a  vacuum  with  a  velocity  of  800  miles  per 
hour,  and  this  is  therefore  the  maximum  limit  of  speed. 
It  is  probable,  however,  that  a  railroad  which  approxima- 
ted to  this  speed  would  find  but  few  passengers,  and  a  mile 
in  62  seconds,  or  58  miles  per  hour,  is  the  nearest  ap- 
proach to  it  yet  made. 

The  vacuum  may  be  made  not  only  by  working  an  air- 
pump  by  a  steam  engine  or  by  water-wheels,  but  by  fill- 
ing an  air-tight  vessel  with  water,  subsequently  allowed  to 
run  out  at  a  depth  greater  than  that  at  which  the  atmo- 
sphere will  support  a  column  of  it. 

The  time  required  to  exhaust  a  3  mile  length  of  pipe, 
by  the  usual  air-pump,  is  4  minutes.  Allow  5  minutes 
for  the  train  to  pass,  and  the  4  minutes  needed  to  exhaust 
the  pipe  again,  would  give  9  minutes  as  the  least  possible 
interval  between  the  starting  of  trains,  since  only  one 
train  at  a  time  can  be  on  any  one  length  of  pipe.  The 
application  of  this  system  to  a  Broadway  railway,  as  has 
been  suggested  by  some  projectors,  would,  for  this  reason, 
be  wholly  impracticable. 

The  principal  advantages  claimed  for  the  Atmospheric 
Railroad  by  its  advocates  are  the  following : 

Its  cars  can  ascend  any  inclination  however  steep ; 
sinc'e  the  force  capable  of  being  applied  does  not  depend 
at  all  upon  the  adhesion  of  the  wheels  to  the  rails,  as  in 
the  case  of  locomotives.  At  a  certain  degree  of  steep- 
ness locomotive  engines  could  not  carry  up  themselves, 
much  less  a  load  ;  while  the  piston  of  an  Atmospheric 
Railroad  would  exert  equal  force  if  its  pipe  were  even 


ATMOSPHERIC    POWER.  <*39 

vertical,  though  of    course  with   much  less    profitable 
effect. 

The  engine  and  tender  being  dispensed  with,  the  force 
which  would  have  been  expended  in  moving  their  weight 
of  20  or  30  tons,  is  so  much  clear  saving. 

The  rails  may  be  made  much  lighter  and  will  last  much 
longer,  where  they  have  not  to  sustain  the  shocks  of  the 
locomotive,  which  is  the  most  powerful  agent  in  their  de 
struclion. 

High  speed  with  locomotives  involves  great  waste  of 
power,  in  consequence  of  the  disadvantageous  velocity 
with  which  the  pistons  must  move.  It  is  not  so  with  the 
atmospheric  system. 

But  greater  safety  is  one  of  the  most  important  recom- 
mendations of  this  system  ;  for  the  cars  cannot  run  off 
the  track,  being  securely  attached  to  the  pipe ;  nor  can 
they  ever  come  into  collision  with  each  other,  for  no  two 
trains  can  be  on  the  same  length  of  pipe  at  once. 

On  the  other  hand,  if  any  obstacle  be  on  the  track, 
there  is  less  power  of  stopping  them,  and  none  at  all  of 
reversing  their  motions  ;  and  the  great  objection  to  the 
stationary  engine  system — that  the  failure  of  one  link  de- 
ranges the  whole  chain — applies  to  this  plan  also. 

But  the  comparative  economy  of  the  Atmospheric  and 
Locomotive  systems  is  the  principal  element  in  deter- 
mining their  relative  merits.  Much  greater  cheapness  of 
working  is  claimed,  by  its  partisans,  for  the  atmospheric 
system,  but  this  is  strenuously  denied  by  other  engineers, 
and  the  testimony  is  so  conflicting  and  varying,  in  conse- 
quence of  the  insufficiency  of  the  data,  that  no  satisfac- 
tory conclusion  can  be  arrived  at.  The  balance  of  argu- 
ment seems,  however,  to  be  against  the  profitable  employ- 
ment of  the  system  in  ordinary  cases.  Under  some  pecu- 


340  RAIL-ROADS. 

liar  circumstances,  however,  such  as  the  case  of  a  line 
with  sleep  grades,  on  which  light  trains  must  be  run  at 
short  intervals,  it  may  probably  be  advantageously  ap 
plied. 

The  longitudinal  valve  being  the  weak  point  of  the  sys- 
tem, several  attempts  have  been  made  to  dispense  with  it. 
The  most  successful  inventions  have  been  those  of  Pil- 
brow  ;  and  of  Julien  and  Vallirio. 

Compressed  air,  Carbonic  acid  gas,  Electro-magnetism 
&c.,  have  been  also  proposed  as  motive  powers  for  railroads, 
but  none  of  them  seem  likely  to  rival,  in  power,  speed,  or 
economy,  that  most  magnificent  and  life-like  of  all  human 
creations,  the  Locomotive  Engine. 


THE   MANAGEMENT    OF    TOWN    ROADS.  34 i 


CHAPTER  VI 

THE    MANAGEMENT    OF    TOWN    ROADS. 

"  The  money  levied  is  more  than  double  of  what  is  necessary  for  exe- 
cuting in  the  completes!  manner  the  work,  which  is  often  executed  in  a 
very  slovenly  manner,  and  sometimes  not  executed  at  all." 

ADAH  SMITH. 

A  WISE  and  well-regulated  system  of  managing  the  re- 
pairs of  roads,  and  of  obtaining  the  greatest  degree  of 
improvement  with  the  least  amount  of  labor,  is  as  impor- 
tant as  their  judicious  construction.  The  "  Road-tax" 
system,  of  personal  service  and  commutation,  though 
nearly  universal  among  us,  is  unsound  in  its  principle, 
unjust  in  its  operation,  wasteful  in  its  practice,  and  unsat- 
isfactory in  its  results.  Borrowed  from  the  "  statute-la- 
bor" of  England,  and  the  "  Corvee"  or  "  Prestation  en 
nature'1''  of  France,  like  them  it  is  a  remnant  of  the  times 
of  feudal  vassalage,  when  one  of  the  tenures  by  which 
land  was  held  was  the  obligation  to  make  the  roads  passa- 
ble for  the  troops  of  the  lord  of  the  manor.  The  evil 
consequences  of  the '  system  will  be  examined,  when  we 
have  briefly  explained  its  organization  in  the  state  of  New 
York,  where  it  has  been  rendered  as  perfect  as  its  nature 
permits.* 

*  A  convenient  edition  of  the  revised  road  act.,  with  commentaries,  &o , 
was  published  at  Rochester  in  1845. 


342       THE  MANAGEMENT  OF  TOWN  ROADS. 

The  directing  power  is  vested  in  "  Commissioners  of 
Highways,"  who  are  chosen  in  each  town  at  the  annual 
town  meeting,  and  have  "  the  care  and  superintendence 
of  the  highways  and  bridges  therein."  Subordinate  to 
them  are  "  Overseers"  of  whom  are  chosen,  at  the  annual 
'  town-meeting,  as  many  as  there  are  road  districts  in  the 
town.  The  commissioners  have  the  authority  to  direct 
the  overseers  as  to  the  grade  of  the  road,  how  it  should  be 
shaped  and  drained,  and  the  like.  They  may  also  lay  out 
new  roads.  The  principal  duties  of  the  overseers  are  to 
summon  the  persons  subject  to  perform  labor  on  the  roads, 
to  see  that  they  actually  work,  and  to  collect  fines  and 
commutation  money.  The  commissioners  are  to  estimate 
the  cost  of  improvements  necessary  on  the  roads  and 
bridges  of  the  town,  and  the  board  of  supervisors  are  to 
cause  the  amount  to  be  levied,  but  within  the  limit,  for  any 
one  year,  of  two  hundred  and  fifty  dollars.  But,  if  a  legal 
town  meeting  so  vote,  the  supervisors  may  levy  "  a  sum 
of  money,  in  addition  to  the  sum  now  allowed  by  law,  not 
exceeding  five  hundred  dollars  in  any  one  }rear." 

"  Every  person  owning  or  occupying  land  in  the  town 
m  which  he  or  she  resides,  and  every  male  inhabitant 
above  the  age  of  twenty-one  years,  residing  in  the  town 
where  the  assessment  is  made,  shall  be  assessed  to  work 
on  the  public  highways  in  such  town."  The  lands  of  non- 
residents are  also  to  be  assessed.  The  whole  number  of 
days'  work  to  be  assessed  shall  be  at  least  three  times  the 
number  of  taxable  inhabitants  in  such  town  ;  and  may  be 
as  many  as  the  commissioners  shall  think  proper. 

Persons  assessed  to  work  on  the  highways,  upon  re- 
ceiving twenty-four  hours'  notice  from  the  overseers,  must 
appear  either  in  person,  or  by  able-bodied  substitutes ;  or 
pay  a  sum  of  one  dollar  for  each  day's  neglect,  unless 


DEFECTS    OF    THE   PRESENT   SYSTEM.  343 

they  shall  have  previously  commuted  at  the  rate  of  sixty- 
two  and  a  half  cents  per  day.  A  team,  cart,  wagon,  or 
plough,  with  a  pair  of  horses  or  oxen,  and  a  man  to  man 
age  them,  satisfies  an  assessment  of  three  days. 

Such  are  the  principal  features  of  the  present  system. 
They  are  all  lefective  in  a  greater  or  less  degree. 

In  the  first  place,  the  condition  of  the  roads,  which  is 
so  important  an  element  of  the  wealth  and  comfort  of  the 
whole  community,  should  not  be  allowed  to  remain  at  the 
mercy  of  the  indolence,  or  false  economy,  of  the  various 
small  townships  through  which  the  roads  pass.  In  one 
town,  its  public  spirit,  wealth,  and  pride,  may  induce  it  to 
make  a  good  road  ;  in  the  adjoining  town,  a  short-sighted 
policy,  looking  only  to  private  interest  in  its  narrowest 
sense,  may  have  led  the  inhabitants  to  work  upon  the  roads 
barely  enough  to  put  them  into  such  a  condition  as  will 
allow  a  wagon  to  be  slowly  drawn  over  them. 

In  the  next  place,  the  "  commissioners"  who  have  the 
primitive  direction  of  the  improvements  and  repairs, 
should  be  liberally  compensated  for  the  time  and  atten- 
tion which  they  give  to  the  work.  Gratuitous  services 
are  seldom  efficient ;  at  best  they  are  temporary  and  local, 
and  dependent  on  the  whims,  continued  residence,  and 
life  of  the  party ;  and  if  the  compensation  be  insufficient, 
the  same  evils  exist  though  in  a  less  degree.  Skill,  labor, 
and  time  cannot  be  obtained  and  secured  without  being 
adequately  paid  for. 

The  third  defect  in  the  system  is  the  annual  election 
of  the  commissioners  and  overseers.  When  men  of 
suitable  ability,  knowledge,  and  experience  have  been 
once  obtained,  they  should  be  permanently  continued  in 
office.  On  the  present  system  of  annual  rotation,  as  soon 
us  the  overseer  has  learned  something  in  his  year's 


344  MANAGEMENT  OF  TOWN    ROADS. 

apprenticeship,  his  experience  is  lost,  and  another  takes  his 
place,  and  begins  in  his  turn  to  take  lessons  in  repairing 
roads  at  the  expense  of  their  condition.  In  other  occu- 
pations, an  apprenticeship  of  some  years  is  thought  ne 
cessary  before  a  person  is  considered  as  qualified  to  prac 
tise  with  his  own  capital ;  while  a  road  overseer,  the 
moment  that  he  is  chosen,  is  thought  fit  to  direct  a  work 
requiring  much  science,  at  the  expense  of  the  town's  cap- 
ital of  time,  labor,  and  money. 

In  the  fourth  place,  the  fundamental  principle  of  the 
Road-tax  is  a  false  one.  Its  contemporary  custom  of  re- 
quiring rents  to  be  paid  in  kind,  has  long  since  been  found 
to  be  less  easy  and  equitable  than  money  rents.  Just  so 
is  work  paid  for  by  the  piece  preferable  in  every  respect 
to  compulsory  labor  by  the  day.  Men  are  now  taken  from 
iheir  peculiar  occupations  in  which  they  are  skilful,  and 
transferred  to  one  of  which  they  know  nothing.  A  good 
ploughman  does  not  think  himself  necessarily  competent 
to  forge  the  coulter  of  his  plough,  or  to  put  together  its 
woodwork.  He  knows  that  it  is  truer  economy  for  him  to 
pay  a  mechanic  for  his  services.  But  the  laws  assume 
him  to  be  a  skilful  road-maker — a  more  difficult  art  than 
plough-making — and  compel  him  to  act  as  one  ;  though 
his  clumsiness  in  repairing  his  plough  would  injure  only 
himself,  while  his  road-blunders  are  injurious  to  the  whole 
community.  Skill  in  any  art  is  only  to  be  acquired  by 
practical  and  successful  experience,  aided  by  the  instruc- 
tions of  those  who  already  possess  it.  An  artisan  cannot 
be  extemporized. 

Fifthly,  labor  by  the  day  is  always  less  profitable  than 
that  done  by  the  piece,  in  which  each  man's  skill  and  in- 
dustry receive  proportionate  rewards.  Working  on  the 
roads  is  generally  made  a  half  holiday  by  those  who  as- 


NEW    SYSTEM    PROPOSED  345 

semble  at  the  summons  of  the  overseer.  Few  of  the  men 
or  horses  do  half  a  day's  work,  the  remainder  of  their 
time  being  lost  in  idleness,  and  perhaps  half  of  even  the 
actual  working  time  being  wasted  by  its  misdirection. 

Lastly,  it  follows  from  the  preceding,  that  the  commu 
tation  system  operates  very  unfairly  and  severely  upon 
those  who  commute  ;  for  they  pay  the  price  of  a  full 
day's  work,  and  their  tax  is  thefefore  doubled. 

Such  are  the  principal  defects  of  the  present  system 
of  managing  the  labor  expended  on  town  roads.  But  it  is 
much  easier  to  discover  and  to  expose,  than  to  remove  them. 
In  the  following  plan  the  writer  has  endeavored  to  com- 
bine the  most  valuable  features  of  the  various  European 
systems,  and  to  adapt  them  to  our  peculiar  institutions. 

In  each  State,  a  general  legislative  act  should  establish 
all  the  details  of  construction,  and  determine  definitely 
"  What  a  road  ought  to  be,"  in  accordance  with  the  theory 
and  practice  of  the  best  engineers.  Surveys  should  be 
made  of  all  the  leading  roads,  and  plans  and  profiles  of 
them  prepared,  so  that  it  might  be  at  once  seen  in  what 
way  their  lines  could  be  most  efficiently  and  cheaply  im- 
proved. 

The  personal  labor  and  commutation  system  should  be 
entirely  abolished.  If  the  town-meeting  would  vote  a  tax 
in  money  of  half  the  amount  now  levied  in  days'  work,  its 
expenditure  under  the  supervision  to  be  presently  de- 
scribed, would  produce  a  result  superior  to  the  present 
one.  When  the  road  is  a  great  thoroughfare,  extending 
far  beyond  the  town,  it  would  be  unjust  to  levy  upon  it  all 
the  expense  ;  and  a  county  tax,  or,  in  extreme  cases,  a 
state  appropriation,  should  supply  what  might  be  necessary. 

In  regulating  the  expenditure  of  the  money  raised,  the 
fundamental  principle,  dictated  by  the  truest  and  most 


MANAGEMENT    OF    TOWN    ROADS. 

far-sighted  economy,  should  be  to  sacrifice  a  portion  of 
the  resources  of  the  road  to  ensure  the  good  employmen. 
of  the  remainder.  The  justice  of  this  principle  needs  no 
argument ;  its  best  mode  of  application  is  the  only  diffi 
culty.  The  first  step  should  be  to  place  the  repairs  of 
the  roads  under  the  charge  of  a  professional  Road-maker 
of  science  and  experience  On  his  skill  will  depend  the 
condition  of  the  roads,  more  than  on  local  circumstances 
or  expenditures.  His  qualifications  should  be  tested  by 
a  competent  board  of  examiners,  if  he  should  riot  have  re- 
ceived special  instructions  in  the  requisite  knowledge, 
such  as  might  well  form  a  peculiar  department  of  educa- 
tion in  our  Colleges  and  Normal  schools.  As  each  town 
by  itself  could  not  afford  to  employ  a  competent  person, 
a  number  of  them  (more  or  less  according  Ho  their  wealth 
and  the  importance  of  the  roads  within  their  bounds) 
should  unite  in  an  association  for  that  purpose. 

The  engineer  thus  appointed  should  choose,  in  each 
township,  an  active,  industrious  man,  of  ordinary  educa- 
tion, to  act  as  his  deputy  in  making  the  expenditures  in 
that  town,  and  as  foreman  of  the  laborers  employed  during 
the  season  of  active  labor  on  the  roads.  This  deputy 
might  be  busily  and  profitably  employed  during  the  en- 
tire remainder  of  the  year,  in  constantly  passing  over  in 
due  rotation  the  whole  line  of  road  under  his  care,  and 
making,  himself,  the  slight  repairs  which  the  continual 
wear  and  tear  of  the  traffic  would  render  necessary.  If 
taken  in  time,  he  himself  could  perform  them  ;  but  if  left 
unattended  to,  as  is  usual,  till  the  season  of  general  re- 
pairs, the  deterioration  would  increase  in  a  geometrical 
ratio,  and  perhaps  cause  an  accident  to  a  traveller,  which 
would  subject  the  town  to  damages  tenfold  the  cost  of 
repairs. 


NEW    SYSTEM    PROPOSED.  347 

The  laborers  hired  by  the  deputy  in  each  town  should 
be  employed  by  piece-work  as  far  as  is  possible.  This 
can  be  carried  out  to  a  great  extent,  when  the  superin 
tendent  is  competent  to  measure  accurately  the  various 
descriptions  of  work,  and  to  estimate  their  comparative 
difficulty.  When  the  work  cannot  be  properly  executed 
by  portions  allotted  to  one  man,  it  may  be  takan  by  gangs 
of  four  or  five,  who  should  form  their  own  associations, 
make  a  common  bargain,  and  divide  the  pay.  In  work 
not  susceptible  of  definite  calculation  as  to  quantity  or 
quality,  and  in  such  only,  day-labor  may  be  resorted  to 
under  a  continual  and  vigilant  superintendence. 

In  such  a  system  as  has  been  here  sketched,  the  money 
tax  would  be  found  to  be  not  only  more  equitable  than  the 
personal-labor  system,  but  even  less  burdensome.  None 
of  it  would  be  wasted  ;  and  those  who  had  skill  and 
strength  for  road-work  would  receive  back,  in  wages, 
more  than  their  share  of  it ;  those  who  were  skilful  in 
other  work  might  remain  at  that  which  was  most  profitable 
to  them,  and  pay  only  their  simple  share  of  the  road-tax, 
not  double,  as  when  they  now  commute  ;  and  the  only 
losers  by  the  change  would  be  the  indolent,  who  were 
useless  under  the  old  system,  but  under  this,  would  be 
obliged  to  contribute  their  share  ;  while  great  gain  in 
every  way  would  ensue  to  the  community  at  large.  The 
subject  urgently  demands  legislative  attention. 


APPENDIX  A.  349 


APPENDIX  A. 


EXCAVATION  AND  EMBANKMENT. 

IT  is  required  to  find  the  content  of  a  mass  of  earth,  filled  into  a 
hollow  or  dug  out  of  a  hill. 

Since  we  cannot  really  measure  the  dimensions  of  the  mass  after 
the  work  is  done,  it  is  necessary  to  determine  the  height  of  the 
original  surface  of  the  ground,  above  (or  below)  some  datum, 
before  the  cutting  or  filling  is  made.  This  is  done  by  taking 
"  levels"  (or  cross-sections)  at  all  points  where  the  ground  changes 
slope. 

After  the  cutting  or  filling  has  been  made,  "levels"  are  again 
taken  over  the  new  surface,  generally  exactly  above,  or  below, 
the  original  ones.  The  difference  of  the  corresponding  levels 
gives  the  desired  heights,  or  depths.  Then  the  proper  rules  of 
mensuration  can  be  applied.  There  are  several  cases  to  be 
considered. 

CASE  I.  "When  the  ground  is  level  transversely,  "  One  level." 
CASE  II.  When  it  is  sidelong,  that  is,  has  a  transverse  slope, 
"  Two  level." 

CASE  III.  "  Three  level"  ground. 
CASE  IV.  Irregular  ground. 
CASE  V.  On  curves. 

CASE  l.—  WMn  ihe  ground  is  level  transversely,  "One  kvel" 
It  is  then  sufficient  to  take  a  single  "  level"  at  each  point  of  the 
line  at  which  the  ground  changes  slope  longitudinally  (as  on 
p.  116).    The  content  is  then  calculated  by  one  of  the  following 
methods : 


350 


APPENDIX  A. 


APPENDIX   A. 


351 


CALCULATION    OF    EXCAVATION    AND    EMBANKMENT. 


1 

Sta- 
tion. 

2 

3 

4 

5 

6 

Cut. 

-f 

7 

8 

9 

10      ! 

Distance. 

Around 
above 

fine™ 

Rire  or  fai; 

Height  of 
grade 
.bore  da- 

End 
Areai. 

Embankment 
Cubic  feet. 

1 

2 
3 

4 
5 
6 

7 

561 

858 
825 
820 
825 
330 

4219 

46.0 
59.2 
53.9 
26.9 
0.9 
4.9 
10.0 

—  4.8 
—  73 
—  7.0 
—  7.0 
—  7.0 
—  25 

46.0 

33.9 
26.9 
19.9 
12.9 
10. 

0 
18 
90 
0 

ooo  too  ' 

0 
1386 
1600 
0 
1672 
528 
0 

388,773 
1,280,994 
660,000 

685,520 
907.500 
87,120 

36.0 

2,329,767 

1,680,140 

In  the  above  tabular  view,  the  first  seven  columns  are  transferred 
from  page  116.  The  remaining  columns  of  areas  and  cubical  con 
tents  are  filled  up  by  the  following  calculations,  assuming  at  50  feet 
the  width  of  road-bed  ;  which  will  be  the  bottom  of  a  cutting,  01 
the  top  of  an  embankment,  at  a  height  just  sufficient  to  equalize  the 
elevations  and  depressions  of  the  final  transverse  profile  of  the  sur- 
face of  the  road.  The  side-slopes  of  the  excavations  are  supposed 
to  be  If  to  1,  and  those  of  the  embankments  2  to  1.  We  are  now 
prepared  to  take  up,  in  turn,  each  of  the  four  usual  methods  of  cal 
dilution* 


23 


352 


APPENDIX  A. 


1.    CALCULATION    BY    AVERAGING    END-ARIAS. 

At  station  1  there  is  neither  jutting  nor  filling.    The  end-area  in 
column  8,  opposite  that  station,  is  therefore  0. 

Fig.  146. 
104. 


50. 
oo 
50. 


At  station  2,  the  cross-section  of  the  excavation  is  shown  in  the 
figure.  The  "  Distances  out"  of  the  side-slopes  are  HX  18  =  27 
feet.  The  top  width  is  therefore  27  -f  50  +  27  =  104  feet.  The 

area  equals —  X  18  =  1386 ;    or    otherwise,  since  the  two 

triangular  portions  equal  a  rectangle  of  the  same  base  and  height 
as  one  of  them,  the  area  =  (50  +  \{  X  18)  X  18  =  1386. 

At  station  3,  the  area  equals  (50  +  li  X  20)  X  20  =  1600. 

At  station  4,  the  Excavation  ends,  or  "  runs  out,"  and  the  area 
=  0 

Fig.  147. 


126. 

At  station  5,  the  section  of  the  embankment  is  shaped  as  in  the 
figure,  and  has  an  area  =  (50  +  2  X  19)  X  19  =  1672. 

At  station  6,  the  area  =  (50  -f-  2  X  8)  X  8  =  528. 

At  station  7,  the  area  =  0. 

The  column  of  End-Areas  is  thus  filled. 

The  Cubical  Contents  are  next  to  be  calculated. 

The  mass  between  stations  1  and  2,  has  an  area  of  0  at  one  end, 
and  of  1386  at  the  other,  and  is  561  feet  long.  Its  contents,  by  the 
method  which  we  now  employ,  will  equal  the  average  of  the  two 

0+  1386 


areas,  multiplied  by  the  length  ; 
cubic  feet 


e.,  — ~ X  561  =  388,773 


APPENDIX  A.  353 

The  contents  of  the  second  mass,  that  between  2  and  3,  equals 

13864-  1600 

— X  858  =  1,280,994  cubic  feet. 

The  third  mass  =  — 2+     X  825  =  660,000  cubic  feet. 
Here  the  excavation  ends,  and  the  embankment  begins. 
The  fourth  mass  =  ~^j— X  820  =  685,520  cubic  feet. 

The  fifth  mass  =  16/2  +  528  x  825  _  907,500  cubic  feet 

The  sixth  mass  = — *— X330  =  87,120  cubic  feet. 

These  results,  being  in  cubic  feet,  should  be  divided  by  27,  to 
reduce  them  to  cubic  yards,  the  denomination  in  which  estimates 
are  made  and  contractors  paid.  This  reduction  would  be  facilitated, 
if  the  measuring  tapes  and  rods  were  divided  into  yards  and  their 
decimal  parts  ;  or  if  the  distances  of  the  stations  were  always 
some  multiple  of  54  feet. 

The  results  thus  obtained,  by  averaging  the  end-areas,  exceed 
the  correct  amount,  as  will  appear  from  an  inspection  of  the  figure 
on  the  following  page,  from  which  may  also  be  deduced  the  cor- 
rection to  be  applied. 

This  figure  presents  a  perspective  view  of  a  tapering  prismoidal 
mass,  such  as  is  an  excavation  of  unequal  size  at  its  two  ex- 
tremities ;  ABCD  being  the  area  of  its  largest  end,  and  EFGH  of 
its  smallest.  Conceive  a  plane,  parallel  to  the  base  of  the  cutting 
CDHG,  to  be  passed  through  EF.  It  would  cut  the  larger  end  in 
the  line  IJ,  leaving  below  it  a  quadrangular  prism,  with  equal  bases 
EFGH  and  CDIJ.  Subdivide  the  remaining  figure,  by  raising  the 
vertical  lines  IL  and  JK,  and  passing  a  plane  through  IL  and  E, 
and  another  through  JK  and  F.  The  interior  body  thus  formed 
appears  wedge-shaped,  but  is  a  triangular  prism,  equal  to  half  the 
quadrangular  prism,  which  has  IJKL  for  base,  and  IE  or  JF  for 
height.  There  remain  two  triangular  pyramids, — one  with  base 
ALI  and  vertex  E,  and  the  other  with  base  BJK  and  vertex  F. 

The  prismoid  being  thus  dissected,  the  contents  of  the  quadran- 
gular and  of  the  triangular  prisms  would  be  correctly  obtained  by 
multiplying  the  sum  of  the  bases  or  end-areas  by  one-half  the 


354 


APPENDIX 
Fig.  148 


APPENDIX   A. 


355 


length  ;  but  t«  find  the  contents  of  the  pyramids,  their  bases  should 
be  multiplied  by  one-third  of  their  length.  The  method  of  calcula- 
tion which  we  have  employed  multiplies  the  sum  of  the  end-areas 
of  the  original  figure,  (which  is  composed  of  the  prisms  and  pyra- 
mids which  we  are  discussing)  by  one-half  the  length  ;  and  there- 
fore gives  a  result  too  large  by  the  difference  between  a  half  and  a 
third  —  i.  e.,  by  a  sixth—  of  the  product  of  the  bases  of  the  pyra- 

JK  X  KB  -f-  IL  XLA      JF 
mids  by  their  length  :  i.  e.,  -       —  ^  —          —      ~R  ' 

Representing  by  d  the  difference  of  the  depths  of  the  end  cut- 
tings, the  ratio  of  the  side-slopes  by  *  to  1,  and  the  length  of  the 
cutting  or  filling  by  I,  the  error  in  excess  will  be 
d  X  sd  +  d  X  id       l_  _  sd*l 
2  X  6~     6   ' 


If  this  be  calculated  for  each  mass,  and  subtracted  from  the  results 
previously  obtained  by  averaging  end-areas,  the  remainder  will 
equal  the  result  obtained  by  the  correct  prismoidal  formula,  to  be 
hereafter  examined.  Thus,  for  the  mass  between  stations  1  and  2 

1$  X  18'  X  561 
the   correction  is  -  -  -  =45,441,  —  giving  a  remainder 

=  388,773  —  45,441  =  343,332,  which  is  the  correct  amount.  The 
original  and  corrected  amounts  are  presented  below  in  a  tabular 
form  : 


ORIGINAL  AML'UNT.3. 

COSKECIIONS 

CORRECTED  AMOUNTS. 

Excavation.  Embankment 

Formula. 

Amounts. 

Excavation. 

Embankment. 

388,773 
1,280,994 
660,000 

685,520 
907,500 
87,120 

liX  1»"X561 

45,441 

858 
82,500 

98,673 
33,275 
7,040 

343,332 

1,280,136 
577,500 

586,847 
874,225 
80,080 

6 
1JX  2»X858 

6 

15X20^X825 

6 
2  XI  SPX820 

6 
2  X112X825 

6 
2  X  8PX330 

6 

2,329,767 

1,680,140 

128,799 

138,988 

2,200,968 

1,541,152 

We  thus  see  that  the  method  of  calculating  excavation  and  em 
bankment  by  averaging  the  end-areas,  though  very  generally  used, 


356 


APPENDIX  A. 


is  so  incorrect  that  in  the  present  example  its  excess  over  the  truth 
is  nearly  130,000  cubic  feet  in  the  excavation,  and  140,000  in  the 
embankment,  or  270,000  in  the  whole,  equal  to  10,000  cubic  yards. 
If  this  method  had  been  used  in  estimating  the  payment  due  to  a 
contractor  at  10  cents  per  yard,  he  would  have  been  consequently 
overpaid  $1000. 

2.    CALCULATION    BY    THE    MIDDLE    AREAS. 

The  second  method  of  calculation  is  to  deduce  the  middle  area 
of  each  prismoidal  mass  from  the  middle  height,  or  arithmetical  mean 
of  the  extreme  heights,  and  multiply  it  by  the  length. 

Applying  lias  method  to  the  preceding  example,  and  adopting  tho 
columns  1,  2,  6,  and  7  of  the  table  on  page  116,  we  obtain  the  re- 
sults exhibited  in  the  last  three  columns  of  the  following  table. 


Station. 

Distance. 

2i 

nil. 

Middle 
Heights. 

Middle 
Areas. 

Excavation. 

Embankment. 

1 

2 
3 
4 
5 
6 
7 

561 

858 
825 
820 
825 
330 

0 

18. 
20. 
0 

0 
19. 
8. 
0. 

9 
19 
10 
9.5 
13.5 
4 

571.5 
1491.5 
650. 
655.5 
1039.5 
232. 

320,611 
1,279,707 
536,250 

537,510 

857,587 
76,560 

2,136,568 

1,471,657 

The  following  formulae  show  the  method  of  obtaining  the  "  mid- 
dle areas"  in  the  sixth  column  of  the  above  table. 
Middle  height^    9.  Middle  area  =  (50+  l^X  9)  X  9     =  571.5 
"         "      =19.        "         "     =  (50+1^X19)  X19     =1491.5 

"      =10.        "         "      =(50+11X10)  X 10     =650. 
«         "      =    9.5     "         "      =  (50+2X   9.5)X9.5  =  655.5 
"         "      =13.5     "         "      =  (50+2X13. 5) X 13  5=1039.5 
"         "      =    4.        "         "      =(50+2X4)      X4       =232. 
The  cubical  contents  are  then  calculated  as  follows  : 
571.5X5(1=     320,6 11. 5  cubic  feet. 
1491.5  X  858  =  1,279,707.         "      " 
650.    X  825  =     536,250.         "      " 
655.5  X  820  =     537,510.         "      " 
1039.5  X  825  =     857.587.5       "      M 
232.    X  330  =       76,560.         "      " 


APPENDIX  A.  35? 

The  results  thus  obtained  are  too  small  keir  deficiency  being 
equal  to  just  half  the  excess  of  the  first  metnod.  This  will  appeal 
oy  again  referring  to  the  figure  on  page  352.  It  will  be  seen  thai 
the  contents  of  the  prisms  in  that  figure  will  be  correctly  given  by 
this  method,  but  that  the  deficiency  is  in  the  pyramids.  Calling 

t^eir  middle  heights  - ;  their  middle  widths  will  be  s  ~  ;  their  mid- 

d*  d* 

die  areas  s  -^  ;  the  contents  of  one  of  them  si  -3  ;  and  of  the  two 

o  o 

*l  -  .     But  the  true  contents  of  the  pyramids  is  2  f  — - —  X  —  ) 

cf 
=  si  —  ;    and  the    deficiency  of  the  method  of  middle  areas  is 

9 

tl  erefore  the  difference  between  a  third  and  a  fourth — i.  e.  a  twelfth 
—of  the  product  of  the  bases  of  the  pyramids  by  their  length,  or 

—  .     Corrections  thus  calculated,  and  added  to  the  above  results, 

would  make  them  coincide  with  the  true  ones  given  by  the  pris- 
moidal  formula,  which  we  will  next  consider. 

3.    CALCULATION  BY  THE  PRISMOIDAL  FORMULA. 

The  mass,  of  which  the  volume  is  demanded,  is  a  true  Prismoid, 
and  its  correct  contents  will  therefore  be  given  by  the  well-known 
prismoidal  formula,  which  is  as  follows  : 

Find  the  area  of  each  end  of  the  mass,  and  also  the  middle  area 
corresponding  to  the  arithmetical  mean  of  the  heights  of  the  two 
ends.  Add  together  the  area  of  each  end,  and  four  times  the 
middle  area.  Multiply  the  sum  by  the  length,  and  divide  the  pro- 
duct by  6.  The  quotient  will  be  the  true  cubic  contents  required. 

Applying  this  method  to  the  original  example,  and  adopting  col- 
umns 1,  2,  6,  7,  8,  from  page  349,  and  the  middle  areas  from  paj^e 
354,  we  may  prepare  the  follow  ing  table  : 


APPENDIX   A. 


Station. 

1 

2 
3 
4 
5 

6 

7 

Distance. 

Cut. 

0 
18 
20 
0 

Fill. 

End 
Areas. 

Middle 
Areas. 

Excavation. 

Embankment. 

561 

858 
825 
820 
825 
330 

0 

19 
8 
0 

0 
1386 
1600 
0 
1672 
528 
0 

571.5 
1491.5 
650. 
655.5 
1039.5 
232. 

343,332 
1,280,136 
577,500 

586,847 
874,225 
80,080 

2,200,968 
1,541,152 

1,541,152 

659,816 

The  manner  of  obtaining  the  amounts  in  the  last  two  columns  is 

as  follows  : 

•  56 1 

(0  +  1386  +    571.5  X  4)  X  — -  =     343,332. 
b 

858 
(1386  +  1600  +  1491.5  X  4)  X  —  =  1,280,136. 

825 

(1600  +        0+650      X  4)  X  —  —     577,500. 
b 

(0  +  1672  +    655.5  X  4)  X  -^  =     586,847. 


(1672  +    528  +  1039.5  X  4)  X  -r-  =      874,225. 

b 

oon 

(528  +        0+232      X  4)  X  -^—  =       80,080. 

Whatever  the  shape  of  the  mass  of  earth  intercepted  between 
two  parallel  cross-sections,  it  maybe  divided  into  prisms,  pyramids, 
wedges,  or  frustra  of  pyramids,  to  all  which,  and  therefore  to  the 
entire  mass,  the  prismoidal  formula  may  be  correctly  applied.* 

The  labor  of  the  calculation  may  be  much  lessened  by  the  use 
of  tables,  such  as  those  of  Macneill,  Bidder,  Fourier,  Johnson,  &c. 
A  specimen  of  Macneill's  is  given  at  the  end  of  the  volume. 

The  prismoidal  formula  may  be  readily  deduced  from  the  dis- 
sected figure  on  page  354.  Call  the  height  of  the  lesser  end  h  ;  of 
the  greater  end  g ;  the  breadth  of  base  b ;  the  ratio  of  the  side- 
slopes  to  unity  s;  and  the  length  /.  TherTwe  may  proceed  thus: 


•  Journal  of  the  Franklin  Institute,  January  and  June,  1840 


APPENDIX   A.  359 

Area  of  the  smaller  end  EFGH  =  h  (b  +  ah)  =  bh  +  sh*. 
.-.  Content  of  the  lower  prism  =  (bh  +  sh*)  X  I,  .     .         .     [A] 
Area  of  rectangle  IJKL  =  (b  -f  2sh)  (g—  k)  =  bg  -f  2sgh 
—  bh  —  Zsh*. 

.'.  Content  of  the  upper  prism  =  (l>g+  2sgh—  bh—2sh*)  X-,  [B] 

Bases  of  the   two  pyramids  =  (g  —  A)  X  s(g  —  A)  =  sg*  — 
2sgh  +  sh*. 

.'.  Contents  of  the  pyramids  (sg*  —  2sgh  -f  sh*)  X  r,     .      .    [C] 

Uniting  the  expressions  for  the  partial  contents  [A],  [B],  and 
[C],  and  reducing  them  to  a  common  denominator,  we  get  for  the 
contents  of  the  prismoid, 

—  3bh  —  6sh*  +  2sg*  —  4sgh  +  2*A*)  X  - 

6 


2sh')  X-    ......     [D]. 

This  expression  may  be  decomposed  into  the  following: 
(bh  +  st?  +  bg+  sg*  +  2bg  +  2bh  +  2sgh  +  sg*  +  sV)  X  l-. 

The  first  two  terms  express  the  area  of  the  smaller  end  of  the 
prismoid,  and  the  next  two  the  area  of  the  larger  end.  The  re- 
maining five  terms  may  be  transformed  into 


which  is  the  expression  for  4  times  the  middle  area  ;  thus  giving 
the  prismo  idol  formula. 

The  formula  [D],  giving  the  contents  of  the  prismoid,  may  be 
transformed  into  another,  more  convenient  for  calculation  than  the 
usual  prismoidal  one.  By  separation  into  factors,  it  becomes, 


......     [E] 

•which  gives  the  following 


Add  together  the  squares  of  the  heights  at  each  end,  and  their 
product.  Multiply  the  sum  by  twice  the  ratio  of  the  side-slopes  to 
Mnity  Reserve  the  product.  Multiply  t  le  sum  of  the  heights  by 


300  APPENDIX  A. 

three  times  the  breadth  of  base,  and  add  the  product  to  the  reserved 
product.  Multiply  their  sum  by  the  length  or  distance  between  the 
two  cross-sections,  and  divide  by  six. 

Applying  the  rule  to  the  mass  between  stations  2  and  3,  we  find 
g  =  20,  h  =  18,  b  —  50,  s  =  l£,  1  =  858,  and  the  calculation  is 
made  thus : 

18"  =  324 

20"  =  400 

18  X  20  =  360 

1084  X  2  X  U  =  3252 

18 
20 

38  X  3  X  50  =  5700 

8952 

858 


6)  7680816 
Cubical  contents  =      1280136 

Formula  [E]  may  be  also  transformed  into  the  following  formula;, 
either  of  which  is  more  convenient  for  calculation  than  the  usual 
prismoidal  formula. 

l-  .     .     .     [FJ 
l  .     .     .     [G] 

When  the  side-slopes  are  lj  to  1,  the  preceding  formulae  are 
much  simplified,  for  2s  —  3,  and  the  factor  three  may  therefore  be 
eliminated  from  each  term,  and  one-half,  instead  of  one-sixth  of 
the  length  be  used  as  a  multiplier. 

Formula  [G]  then  becomes 

[Of+  *)'+*(*  +  A)-*A]X-~ 


This  formula  gives  the  following 


APPENDIX   A.  361 

RULE. 

When  t.ie  side-slopes  are  1|  to  1,  add  together  the  breadth  of 
base  and  the  heights  at  each  end  of  the  mass.     Multiply  this  sura 
by  the  sum  of  the  two  heights.     From  the  product  subtract  the  pro- 
duct of  the  two  heights.    Multiply  the  remainder  by  half  the  length. 
The  calculation  of  the  preceding  example  will  then  be  made  thus : 
50 

18         18 
20        20 

88  X   38  =  3344 
18  X   20=    360 

2984 
858-4-    2=    429 

Cubical  contents  =  1,280,136 

When  the  height  and  therefore  area  at  one  end  =  0,  h  vanishes 
from  the  formula  [E],  which  thus  becomes 

(2^  +  3^)  X  -^  =  (2^  +  36)  ^ [I] 

giving  the  following 

RULE. 

Add  the  product  of  the  height  by  twice  the  slope  to  three  times 
the  breadth  of  base.  Multiply  the  sum  by  the  height,  and  that  pro- 
duct by  the  length,  and  divide  the  product  by  six. 

The  calculation  of  the  cubical  contents  of  the  mass  between  sta- 
tions 1  and  2  will  accordingly  be  thus  made : 

2X  liX  18  =    54 

3    X  50  =  150  18  X  561 

204  X 5 =  343332. 

204 

When  these  last  two  conditions  are  combined  (i.  e.  slopes  1^  to  1 
and  one  height  =  0)  formula  [I]  becomes,  still  more  simply, 

(g+Vgl 

a [I'] 


APPENDIX   A. 


FORMULA    FOR    A    SERIES    OF    EQUAL    DISTANCES. 

When  the  cross-sections  have  been  taken  at  uniform  distances 
apart,  (as  is  usual  in  the  final  location  of  a  Road  or  Railroad,  one 
hundred  feet  being  the  customary  interval)  the  calculation  of  the 
cubical  contents  of  the  successive  prismoids  may  be  reduced  to  a 
single  operation  for  the  whole  series,  and  therefore  much  short- 
ened, by  the  use  of  the  symmetrical  formula  which  will  be  now 
investigated,  and  presented  in  the  form  of  a  Rule. 

Through  the  first  prismoidal  mass  of  earth,  conceive  two  verti- 
cal planes  to  pass  lengthwise,  cutting  it  in  the  lines  in  which  the 
side-slopes  meet  the  base  of  the  road,  (which  is  the  bottom  of  an 
excavation,  or  the  top  of  an  embankment)  as  the  lines  CG  and 
DH,  of  Fig.  148.  These  planes  divide  the  prismoid  into  a  cen- 
tral prism,  and  two  pyramids  or  frusta.  The  content  of  the  entire 
prismoid  is  expressed,  according  to  formula  [G],  page  358,  by 


......  [G] 

This  may  be  decomposed  into  these  two  portions  : 


^]  .  .  .  [L] 

Formula  [K]  expresses  the  content  of  the  central  prism,  and  for- 
mula [L]  that  of  the  two  pyramids  or  frusta.  Denoting  the  end 
depths  (without  regarding  which  is  the  greater)  by  h  and  A',  (tho 
former  representing  the  depth  at  the  starting  point,  and  the  latter 
that  at  the  farther  end)  the  formula  become 

[M] 


AA']    .  .  .  [N] 

Considering  now  the  next  prismoid,  or  following  length  of  exca- 
vation, (or  embankment)  its  first  depth  is  seen  to  be  identical  with 
the  last  depth  of  the  preceding  prismoid,  i.  e.  it  is  V.  Calling  tho 


APPENDIX   A.  363 

depth  at  its  farther  end  h",  the  content  of  its  central  prism,  by 
formula  [M],  will  be 


The  content  of  the  third  length  will  similarly  be 
j(h"+h>") 

and  so  on  for  the  succeeding  portions,  /  being  the  same  in  each. 
The  sum  ol  any  number  of  these  will  be 

—  [(A  +  h')  +  (h1  +  A")  +  (A"  4-  A'")  +  &c ] 

=  ^-  (A  -f  2A'  +  2A"  +  2A'"  +  &c.) 

Designating  the  last  depth  of  the  series  by  H,  this  expression 
may  be  written 

bl  (A  +  A'  +  A"  +  A'"  +  A"  +  &c +  ^)  .  .  .  .  [O] 

\  2  2  ' 

Expressed  in  words,  it  then  gives  this 


To  find  the  cubical  contents  of  the  central  prisms,  add  together 
half  of  the  first  and  last  depths,  and  all  the  intermediate  depths. 
Multiply  their  sum  by  the  breadth  of  base,  and  that  product  by  the 
length  in  feet  of  one  of  the  equal  distances.  The  last  product  will 
be  the  contents  in  cubic  feet. 

The  content  of  the  two  pyramids  or  frusta,  on  each  side  of  tho 
central  prism,  is  for  the  first  length,  by  formula  N, 


For  the  second  length  it  is  j[(h'  +  h"f  —  h'h"} 

For  the  third  length  it  is  —  [(h"  +  A'"]a  —  h"h'"~\  ;  and  so  on. 
3 

For  any  number  of  equal  lengths,  the  sum  of  the  contents  is 

?  +  &c.  —  (hhl  +  h'h"  +  &c.)]  .      .  .  [F] 


364  APPENDIX  A. 

Expressed  in  woids,  it  gives  this 


To  find  the  cubical  content  of  the  pyramids  or  frusta,  square  the 
sum  of  the  first  and  second  depths,  the  second  and  third,  the  third 
and  fourth,  and  so  on,  and  add  these  squares  together.  Multiply 
the  first  depth  by  the  second,  the  second  by  the  third,  and  so  on, 
and  add  the  products  together.  Subtract  the  sum  of  the  products 
from  the  sum  of  the  squares.  Multiply  the  difference  by  the  length 
in  feet  of  one  of  the  equal  distances,  and  that  product  by  the  ratio 
of  the  side-slopes  to  unity.  Divide  the  last  product  by  three,  and 
the  quotient  will  be  the  content  in  cubic  feet. 

The  sum  of  the  two  contents,  thus  obtained  by  formulae  [O]  and 
[P],  or  by  the  Rules  derived  from  them,  will  be  the  total  content 
required. 

In  the  following  example,  the  width  of  base  is  30  feet,  the  side- 
slopes  2  to  1,  and  the  equal  distances,  at  which  the  levels  were 
taken,  are  each  100  feet.  Therefore  J  —  30,  s  =  2,  I  =  100,  and 
A,  A',  h"  =  the  successive  numbers  in  the  third  column  of  the  table. 
In  substituting  the  values  of  the  quantities  in  the  formulae  they  will 
be  more  conveniently  written  under  each  other. 


Station. 

Distance. 

Depth. 

1 
2 
3 
4 
5 
6 
7 

100 

100 
100 
100 
100 
100 

0  =  A 
2.  =  A' 
4.=  A" 
3.  =  A'" 
5.  =hv 

i.  =AV 

4.  =H 

The  content  of  the  central  prism,  by  formula  [O],  = 

0. 

+  2 
+  4 
+  3 
+  5 


17  J 


30  X  100  X 


>  =  30  X  100  X  17  .  =  51000   cubic  feet. 


APPENDIX  A. 


365 


The  contents  of  the  pyramids  and  frusta,  by  formula  [P], 


2  X  100  ^ 

r     (o  +  2)'] 

+  (2  +  *)' 
+  (4  +  3}' 
+  (3  +  5)* 
+  (5  +  1)' 
+  (1  +  4)'J 

2X4 

+  4X3 

3 

+  5X1 
+  1X4 

r    "  4 

. 

+  36 

8 

+  49 
+  64 

+  12 
+  15 

200 
=  —  X  170=11333. 

+  36 

+    5 

3 

+  25 

+    4 

1    214 

I      44J 

51000+  11333.  =62333  cubic  feet  =  2308.6  cubic  yards  = 
the  entire  cubical  content  required. 

4.    CALCULATION    BY    MEAN    PB^OPOR  FIONALS. 

A  fourth  method,  called  that  of  "  Mean  proportionals,"  is  som»> 
times,  though  very  improperly,employed.  It  assumes  implicitly  that 
the  mass  is  a  frustum  of  a  pyramid,  i.  e.  that  all  its  sides,  if  pro- 
duced, would  intersect  in  one  vertex,  a  supposition  which  would 
very  seldom  be  perfectly  true.  On  this  assumption  the  following 
is  the  Rule. 

Add  together  the  areas  of  the  two  ends,  and  a  mean  proportional 
between  them,  (found  by  extracting  the  square  root  of  their  product) 
and  multiply  the  sum  of  these  three  areas  by  the  length  of  the 
frustum,  and  divide  the  product  by  three.  The  result  is  always 
much  less  than  the  truth,  for  it  treats  as  pyramids,  or  thirds  of 
prisms,  the  wedge-shaped  pieces  which  are  really  halves  of  prisms. 
It  is  farthest  from  the  truth  when  one  of  the  areas  =  0. 

CASE  II. —  When  the  ground  is  sidelong,  i.e.,  ha*  a  transverse  slope, 

"  7ico-level." 

The  cross-section  of  the  ground,  at  right  angles  to  the  direction 
of  the  road,  has  been  assumed  to  be  level.  But  the  height  of  the 
surface  of  the  ground  usually  varies  considerably  within  the  width 
to  be  occupied  by  the  future  road,  and  renders  necessary  the  talcing 
of  levels  not  merely  on  the  centre  line,  but  also  on  the  sides  at  the 


366  APPENDIX  A. 

points  in  which  the  side-slopes,  of  the  cuttings  or  fillings  of  the 
road,  would  intersect  the  surface  of  the  ground. 

1.  When  the  surface  of  the  ground  nas  the  same  slope  at  each 
end  of  the  mass  t  j  be  calculated. 

On  such  ground  if  the  centre  level,  i.  e.,  the  height  or  depth  on 
the  centre  line  of  the  road,  be  used  to  calculate  the  area  of  the 
cross-section,  as  if  the  ground  were  level  transversely,  the  area 
thus  obtained  will  always  be  too  small;  the  difference  being  etpial 
to  the  triangle  DQR,  in  Fig.  149. 


This  must  be  guarded  against  in  calculating  the  content  from  a 
preliminary  survey,  in  which,  usually,  only  one  single  level  is 
taken  along  the  centre  line  at  each  station. 

If  the  average  of  the  extreme  heights  is  taken  and  used  to  get 
the  area,  as  if  that  were  the  height  of  a  level,  horizontal,  transverse 
section,  the  result  is  always  too  great. 

There  will  then  be  some  height,  which  used  as  the  height  of  a 
section  level  transversely,  will  produce  the  true  area.  This  is 
called  the  equivalent  mean  height.  One  method  for  determining 
the  true  area  is  the  following : 

Fig.  150. 


The  cross-section  ABCD  =  (EC  x  £DF)  +  (BF 
2.  When  the  transverse  slope  of  the  ground  is  not  the  same  at 
each  end  of  the  mass. 
In  this  case  the  surface  of  the  ground  is  warped  or  twisted,  being 


APPENDIX   A.  367 

ft  hyperbolic  paraboloid,  but  the  prismoidal  formula  still  applies, 
as  will  now  be  shown. 

THE    CALCULATION    OF    ROAD  EXCAVATIONS    AND    EMBANKMENTS, 
WHEN  THE  GROUND  IS  A  WARPED  SURFACE.* 

When  an  engineer  is  laying  out  a  road  or  railway,  he  has  to 
determine  the  amount  of  earth  necessaiy  to  be  removed  in  making 
the  "  cuts"  and  "  fills"  of  the  road.  To  do  this,  his  most  usual 
course  is  to  take  "  cross-sections"  or  "  profiles,"  of  the  ground  at 
right  angles  to  the  line  of  road,  at  convenient  intervals,  and  then  to 
calculate  by  various  methods,  commonly  near  approximations,  the 
volume  included  between  each  pair  of  these  cross-sections.  The 
distances  apart  at  which  these  cross-sections  are  taken,  are  deter- 
mined by  the  engineer  according  to  the  nature  of  the  ground  ;  his 
aim  being  that  there  shall  not  merely  be  no  abrupt  change  of 
height  between  each  pair  of  these  cross-sections,  but  that  the  sur- 
face from  one  to  the  other  shall  vary  uniformly ;  gradually  passing, 
for  example,  from  a  small  to  a  great  degree  of  slope,  or  from  a 
slope  to  the  right  into  a  slope  to  the  left,  without  any  sudden 
variation  at  any  one  place. 

The  surface  fulfilling  this  condition  of  varying  uniformly,  since 
it  is  everywhere  straight  in  some  direction,  is  evidently  a  ruled 
surface;  and  since  the  extreme  profiles  are  seldom  parallel,  it  will 
be  a  warped  or  twisted  surface. 

Our  engineers  have  been  accustomed  to  consider  these  surfaces  as 
not  admitting  of  precise  calculation,  but  only  of  a  degree  of  ap- 
proximation varying  with  the  nearness  of  the  cross-sections.  The 
object  of  this  paper  is  to  examine  the  correctness  of  this  position. 
It  will  therefore  have  two  parts :  firstly,  a  discussion  of  the  precise 
nature  of  the  surface  ;  and  secondly,  an  investigation  of  a  formula 
applying  to  it. 

I.  What  sort  of  a  warped  surface  is  the  one  in  question;  that  -is, 
what  is  its  mode  of  generation  ? 

To  determine  this,  we  must  inquire  what  the  engineer  means 

*  This  paper  was  read  by  Prof.  Gillespie  before  the  "  American  Association 
for  the  Advancement  of  Science,"  and  it  has  been  thought  beet  to  insert  it 
without  abridgment  or  alteration.— -ED. 


368 


APPENDIX   A. 


when  lie  says  that  the  ground  "  varies  uniformly"  from  the  place 
at  which  he  stands,  and  at  which  he  has  just  taken  a  cross-section, 
to  the  place  at  which  he  decides  it  will  be  proper  to  take  the  next 
cross-section ;  whether  he  means  that  the  ground  between  the  two 
is  straight  cross-wise  or  straight  length-wise;  straight  at  right  angles 
to  the  direction  in  which  the  road  runs,  or  straight  in  that  direction. 
Probably  few  engineers  ask  themselves  this  question  in  so  many 
words ;  but  it  would  seem  that  the  former  conception,  or  straight- 
ness  cross-wise,  is  the  Fig.  151. 
more  likely  to  be  what 
is  meant,  for  the  reason 
that  any  deviation  from 
straightness  in  that 
direction,  at  right 
angles  to  the  line 
along  which  we  look, 
is  much  more  easily 
seen  than  in  the  other 
direction.  We  can 
therefore  much  more  readily  determine  whether  the  surface  of  the 
road  is  straight  or  curved  from  side  to  side  than  from  end  to  end ; 


\ 

\ 

\ 

\ 

\ 

\ 

Fig.  152. 


\ 


and  the  surface  which 
we  pronounce  uniform, 
is  therefore  much  more 
likely  to  be  straight 
cross-wise,  than 
straight  length-wise. 

In  geometrical  lan- 
guage the  former  sur- 
face (which  is  repre- 
sented in  plan  in  Fig. 
151,)  is  generated  by  a 

straight  line  resting  on  the  two  straight  lines  which  join  the 
extremities  of  the  two  profiles,  and  moving  parallel  to  their  planes 
or  perpendicular  to  the  axis  of  the  road.  This  surface  is  a  "  hyper- 
bolic paraboloid.'" 

The  latter  surface  (shown  in  plan  in  Fig.  152,)  is  generated  by  a 
straight  line  .vesting  on  the  two  profiles,  and  moving  parallel  to  the 


APPENDIX   A. 


369 


vertical  plane  which  passes  through  the  axis  of  the  road.  It  also 
is  a  hyperbolic  paraboloid,  though  a  different  one  from  the  former. 
1  he  French  engineers  Fig.  153. 

(f-'ganzin  1, 114 ;  VEcole  \ 

Centrale,  etc.,)  adopt\     \ 
this  latter  hypothesis.    \ 
"We  have    seen,  how-      \ 
ever,  that  the  former  is        \ 
the  more  probable  one. 
The  French  hypoth- 
esis   is   farther    objec- 
tionable     on     mathe- 
matical   grounds.     As 


soon  as  the  generating  line  quits  the  end  lines  and  rests  on  the 
side  lines,  it  has  new  directrices,  and  the  whole  surface  generated, 
is  really  composed  of  three  different  paraboloids ;  a  want  of  sym- 
metry alone  is  sufficient  to  cause  the  rejection  of  this  system. 

Fortunately,  the  practical  difference  between  the  two,  is  really 
very  slight;  for  a  very  small  change  in  the  latter  h}-pothesis  will 
make  its  result  identical  with  that  of  the  former.  Conceive  the 
straight  line  which  rests  on  the  two  profiles  to  move  on  them  in 
such  a  way  as  always  to  divide  them  proportionally,  as  in  Fig.  153. 
The  surface  thus  generated  is  identical  with  that  of  Fig.  151  ;  as  is 
proven  in  the  higher  descriptive  geometry. 

This  last  conception  is  also  more  probably  correct  than  Fig.  152 — 
even  if  we  suppose  the  engineer  to  consider  longitudinal  straight- 
ness,— since  he  is  more  likely  to  extend  his  imagination  from  all 
parts  of  one  profile  to  the  corresponding  parts  of  the  other,  than  in 
lines  perpendicular  to  the  profile  on  which  he  stands.* 

II.   We  will  tJierefore  now  proceed  to  investigate  the  content  of  a 

*  Since  the  above  was  written,  the  author  has  seen  an  abstract  of  the  Lectures 
on  Roads,  given  at  "  L'Ecole  des  Fonts  f.t  Chawtees,"  (the  highest  authority  on 
puch  matters  in  France,  and  therefore  in  the  world),  in  which  this  last  hypothe- 
sis is  adopted.  This  removes  the  only  obstacle  to  the  acceptance  of  the  princi- 
ple which  is  here  advocated. 

In  the  models  illustrating  the  original  paper,  the  surfaces  in  question  were 
formed  by  silk  threads,  representing  the  generating  line?.  The  identity  of  the 
first  and  third  surfaces,  and  the  dissimilarity  of  the  second,  were  then  evident 
on  mere  inspection. 

16* 


370 


vPPENDIX  A. 


aolid,  bounded  on  one  face  by  a  warped  surface  generated  on  the  first 
hypothesis— the  other  faces  being  planes. 

"We  will  take  the  case  of  an  excavation ;  that  of  an  embankment 
being  the  same  inverted. 

"We  will  begin  by  considering  the  bottom  of  the  excavation  to  be 
level,  and  its  sides  to  be  vertical ;  and  will  afterward  discuss  the 
more  usual  form. 

Pig.  154. 


Let  A  and  A'  be  the  parallel  sections  at  each  end  of  the  solid  ;  4 
and  b'  their  respective  breadths  ;  p  and  g  the  outside  depths  of  the 
section  A,  and  p'  and  q'  those  of  the  section  A'  ;  and  I  the  length  of 
the  solid,  measured  at  right  angles  to  the  planes  of  the  sections. 

The  outside  depths  are  supposed  to  vaiy  uniformly  from  p  to  p' 
and  from  q  to  q'. 

Then,  at  x  feet  from  A,  the  breadth  =  b  +  —(br—  b)  ;  one  outside 
depth 

=  p+  —  (p'  —  p)  ;  and  the  other  =  q  +  ^-  (qr—  q). 

The  area  of  that  section  will  therefore  be 

6+JL6'-J       x          +  ?L>-       + 


Arranging  this  expression  according  to  the  powers  of  a,  it  be- 
comes, 


APPENDIX    A.  371 


+  (b'-b)(p'-p  +  g'-q)  ^  n 

The  product  of  this  by  dx  being  the  differential  of  the  solid,  the 
required  volume  is, 


Integrating  from  o  to  Z,  we  obtain  this  expression, 


Performing  the  operations  indicated  and  factoring,  we  finally  ob- 
tain for  the  required  volume  of  the  solid,  this  symmetrical  formula. 


"NVe  now  propose  to  show  that  the  volume  given  by  the  preced- 
ing formula  (3)  is  the  same  as  would  be  obtained  by  applying  the 
familiar  prismoidal  rule  to  the  given  solid. 

The  area  of  the  section  A  =  4  b  (p  +  q);  and  that  of  the  section 

A'  =|  &'(?'  +  ffO- 
The  area  of  the  section  midway  between  A  and  B, 


*  Two  particular  cases  of  this  general  formula  are  worthy  of  special  notice. 

Lf.i  the  base  of  the  given  solid  be  a  parallelogram, 

Then  b=b'  ;  and  formula  (3)  becomes, 

1/t  I  [*/»  &  (P  +  ?)  +  Vs  ft  (P'  +  «')]  I  =*  I  +  l/4  (P  +  7  +  P'  +  gO  =  The  product  of 
the  base  of  the  warped  surface  prism  by  the  arithmetical  means  of  the  heights  of 
its  four  summits. 

Let  the  base  be  a  triangle. 

Then  V  =  o.  and  p'=  q'  ;  and  formula  (3)  becomes, 

*/V  I*  (P  +  ff)  +  *  P*]  =  1A  *  l  x  V»  (P  +  9  +  PO  =  The  product  of  the  base  by 
the  arithmetical  mean  of  the  heights  of  the  three  summits. 

These  two  formulae  are  also  true  when  the  upper  surface  of  the  prism  is  a 
plane,  since  a  plane  is  only  a  particular  case  of  a  hyperbolic  paraboloid.  They 
thus  give  a  general  proof  of  the  well  known  rules  for  the  content  of  truncated 
Dr'miiF.  which  have  triangles  or  parallelogram?  for  bases. 


372  APPENDIX  A. 

Adding  together  the  areas  of  A  and  A',  and  four  times  the  middle 
area,  and  multiplying  the  sum  by  £  I,  we  obtain, 

tf(bp  +  bq  +  b'p'+  5Y  +  ^bp'  +  $bq'  +  \Vp  +  \Vtf) 
which  can  be  decomposed  into  the  following : 

i'[(m&')0>  +  ff)  +  (*'+iW  +  2')]     •    •    •    •  (30 

This  expression  is  identical  with  the  general  formula  (3)  before 
obtained. 

"We  thus  arrive  at  the  conclusion  that  the  familiar  "prismoidal 
formula"  can  be  applied  with  perfect  accuracy  to  such  solids  as  we 
have  discussed,  having  one  of  their  faces  a  warped  surface  generated 
as  in  our  first  or  third  hypothesis. 

We  have  thus  far  been  supposing  that  the  road-bed  was  hori- 
zontal, or,  in  more  general  terms,  that  the  base  of  the  solid  was 
perpendicular  to  its  ends.  The  base  may,  however,  make  oblique 
angles  with  them.  Then,  to  reduce  the  solid  which  we  have  been 
discussing  to  this  form,  we  must  take  from  it  a  wedge-shaped  solid, 
the  breadths  of  whose  ends  are  b  and  U,  and  one  of  whose  depths 
is  zero. 

But  the  prismoidal  rule  also  applies  to  this  wedge,  and  therefore 
to  the  solid  which  remains  after  it  is  taken  away  from  our  original 
solid ;  since  all  the  areas  enter  the  formula  only  by  addition  or 
subtraction,  with  a  common  multiplier. 

Again,  the  solids  occurring  in  excavations  and  embankments 
usually  have  sloping  sides  (as  shown  by  the  dotted  lines  in  figures 
154  and  155),  instead  of  the  vertical  sides  which  we  have  used  hi 
our  investigation. 

But  the  solids  to  be  removed  to  reduce  our  original  solid  to  this 
form,  are  frusta  of  pyramids,  to  which  the  prismoidal  formula  also 
applies,  and  therefore  to  the  new  solid  in  question ;  for  the  reasons 
given  in  the  preceding  paragraph. 

We  will  take  as  an  example  an  excavation  of  which  A  and  A' 
are  cross-sections,  100  feet  apart.  All  the  dimensions  will  be  in 
feet.  In  section  A,  Fig.  154,  let  p  =  6  and  q  =  15.  In  section  A',  Fig. 
155,  let  p'  =  18,  and  q'  =  12.  The  sections  have  the  side  slopes,  1  to 
1,  shown  by  the  dotted  lines.  The  bottom  width  of  each  =  18. 

Then,  the  area  of  A  =  279,  and  that  of  A' =  486.    The  middle 


APPEXDIX   A.  373 

area,  obtained  from  the  mean  of  the  outside  depths  (-£  x  (6  +  18) 
=  12,  and  i  x  (15  +  12)  =  13.5)  is  391.5. 

Then  the  content  of  the  solid  by  the  prismoidal  rule  =  38,850 
cubic  feet. 

The  same  rule  can  be  applied  directly  to  "  Three-level  ground" 
i.  e.,  ground  given  by  cross-sections,  in  which  three  levels  have 
been  taken,  viz.,  one  at  the  centre,  and  one  on  each  side  at  the 
points  where  the  side  slopes  meet  the  natural  surface.  The  middle 
cross-section  being  obtained  from  the  mean  of  the  levels  at  each 
end,  the  prismoidal  rule  can  be  at  once  applied. 

In  the  case  of  "  Irregular  cross-sections,"  in  which  the  inequali- 
ties of  the  surface  of  the  ground  have  rendered  it  necessary  to  take 
more  than  these  three  levels,  the  rule  will  still  apply  after  the  fol- 
lowing preparation.  Conceive  a  series  of  vertical  planes  to  pass 
through  all  the  points  on  each  cross-section,  at  which  the  trans- 
verse slope  of  the  ground  changes,  and  at  which,  therefore,  levels 
have  been  taken,  and  to  cut  the  other  cross-section  so  as  to  divide 
the  widths  of  the  two  proportionally. 

Then  the  surfaces  between  these  planes  may  be  regarded  as 
generated  on  our  third  hypothesis,  and  can  therefore  be  calculated 
by  the  prismoidal  rule ;  since  it  has  been  shown  to  apply  to  the 
surfaces  of  the  first  hypothesis,  and  these  are  known  to  be  identi- 
cal with  those  of  the  third.  Thus,  considering  the  ground  on  one 
side  of  a  centre  line,  let  one  cross-section  have  depths  of  6.00  in 
the  centre,  and  10.00  outside  cutting.  Let  the  other  end  be  8.00  in 
centre,  12.00  at  four  feet  from  centre,  and  6.00  outside  cutting. 
Let  the  half  width  of  road  bed  be  10  feet,  and  side  slopes  1  to  1. 
Then  the  vertical  plane  passing  through  the  12.00  level,  at  4  feet,  a 
quarter  of  the  whole  width  (10  +  6),  from  centre,  should  cut  the  other 
section  at  one-quarter  its  width  (10  +  10),  or  5  feet,  from  centre. 
The  depth  at  this  point  would  be  6  +  i  (10  —  6)  =  7.00.  This  enables 
us  to  get  a  middle  area ;  its  depth  being  i  (8  +  6)  at  centre,  |  (12  +  7) 
at  \  (4  -f  5)  from  centre,  and  \  (6  +  10)  at  the  outside  cutting. 

The  prismoidal  rule  can  now  be  used.  A  similar  preparation  for 
calculating  can  be  applied  to  cross-sections  composed  of  any  num- 
btr  of  levels.  The  labor  is  much  less  in  practice  than  it  appears  hi 
description. 


374  APPENDIX   B. 

If  the  views  here  presented  should  meet  with  general  accept- 
ance, engineers  would  be  enabled  to  economize  much  time  and 
labor,  since  they  would  no  longer  feel  themselves  under  the  neces- 
sity of  taking  their  cross-sections  so  near  together  that  the  ground 
between  them  should  be  approximately  plane,  but  could  take  them 
as  far  apart  as  the  ground  varied  uniformly,  no  matter  how  much 
or  how  far  that  might  be. 

It  is  now  proposed  to  compare  the  results  given  by  this  rule  with 
those  obtained  by  the  usual  methods,  and  to  establish  formulas  by 
which  the  nature  and  the  amount  of  the  errors  which  these  latter 
involve  can  be  determined  in  advance. 

A  type  of  the  solids  in  question  is  represented  in  Fig.  156,  as  an 
excavation  seen  in  perspective.  Inverted,  it  will  represent  an  em- 
bankment. 

To  simplify  the  investigation,  we  will  conceive  the  side-slopes 
to  be  prolonged  till  they  meet,  as  shown  by  the  broken  lines  in  the 
figure.  The  conclusions  at  which  we  may  arrive  respecting  the 
new  solid  thus  produced,  will  apply  equally  well  to  the  original 
one,  since  the  triangular  prism  which  we  imagine  added,  is  com- 
mon to  both  the  solids  discussed,  whatever  hypothesis  we  may 

Fig.  156. 


vi Jl^L'_-i i 

•<     «P   x       #Q      > 

adopt  respecting  their  upper  surfaces.  The  additional  depth  is 
equal  to  the  bottom  width  divided  by  twice  the  ratio  of  the  base 
of  the  side-slopes  to  their  height,  or  to  b  -H  2  «,  in  the  usual  sym- 
bols. We  will  suppose  the  original  outside  depths  p,  g,  p',  gf,  of 
the  end  sections,  to  be  increased  by  this  quantity,  and  will  call 
these  new  depths,  p  and  Q  for  one  section,  and  P'  and  Q'  for  the 
other. 


APPENDIX    A.  375 

Then  the  area  of  the  triangle  which  forms  one  end  of  the  new 
solid,  is  the  difference  between  the  trapezoid  whose  parallel  sides 
are  p  and  q,  and  the  two  triangles  which  have  P  and  Q  for  their 
altitudes,  and  «  p  and  *  Q  for  their  bases,  and  is 

HP   +   Q)   *  (*  P  +  *  Q)  —  iPX*P-iQXSQ=SPQ. 

Similarly,  the  other  end  area  is  s  p'  Q'.  The  middle  section  will 
have  the  outside  depths,  i  (p  +  P')  and  i  (q  +  Q').  Consequently 
its  area  is 

s  x  |  (P  +  P')  x  |  (Q  +  Q')  =  i  s  (p  +  p')  x  (Q  +  Q'). 

The  true  content  of  the  solid  under  consideration  will  then  be 

£  I  [s  p  Q  +  s  P'  Q'  +  4  x  i  s  (P  +  P')  x  '(Q  +  Q')] 

=  &  s  I  (2  P  Q  +  2  P'  Q'  +  P  q'  +  P'  Q) (1) 

We  are  now  prepared  to  compare  with  this  correct  result  those 
given  by  each  of  the  usual  methods  of  calculation. 

I.  The  method  of  "  averaging  end  areas"  will  first  be  examined. 
This  considers  the  content  of  the  solid  to  equal  the  product  of  the 
half  sum  of  its  end  areas  by  its  length  ;  i.  e.,  using  the  same  sym- 
bols as  above, 

iZ(«pQ  +  «p'QO (2) 

The  excess,  if  any,  of  the  true  content  above  this,  will  therefore 
be  obtained  by  subtracting  (2)  from  (1).  It  is  found,  after  a  little 
reduction,  to  be 

£  s  I  (P  Q'  +  P'  Q  -  p  Q  —  p'  Q') (3) 

The  value  of  this  expression  is  not  changed  by  substituting  in  it 
the  original  depths  for  the  increased  depths  (owing  to  its  sym- 
metrical character),  and  it  then  becomes, 

\sl(pq'  +  p'  q-pq  —  p'  q') (b') 

We  infer  from  this  formula,  that  tJie  true  content  exceeds  the  content 
given  by  "  Averaging  end  areas"  whenever  p  tf  +  p'  q  >  p  q  +  p'  q'; 
i.  c.,  whenever  the  sum  of  ike  products  of  the  pairs  of  depths  (or 
Jieights)  diagonally  opposite  to  each  other,  is  greater  than  the  sum  of 
the  products  of  those  belonging  to  the  same  cross-section.  When  the 
former  sum  is  the  smaller,  then  the  true  result  is  the  smaller.  The 
two  sums  are  the  same,  and  the  results  therefore  equal,  only  when 
p  =  p'  or  q  =  q';  i.  e.,  when  the  depths  on  one  or  the  other  side 
of  the  solid  are  the  same. 
It  is  so  well  known,  however,  that  the  method  of  "  averaging 


376  APPENDIX  A. 

end  areas"  always  gives  more  than  the  true  content  of  a  prismoid 
(such  as  a  tapering  stick  of  timber,  a  mill-hopper,  etc.),  that  there 
seems  at  first  glance  an  apparent  inconsistency  in  the  above  state- 
ment. The  difficulty  is  removed,  however,  by  the  consideration 
that  our  warped-surface-solid  is  not  a  prismoid,  although  it  is  to  be 
calculated  by  the  prismoidal  rule.  A  somewhat  analogous  case  is 
that  of  a  sphere,  to  which  the  prismoidal  rule  also  applies,  as  shown 
in  an  ingenious  paper  by  Mr.  Ellwood  Morris. 

II.  The  method  of  "  Middle  areas"  will  next  be  taken  up.    This 
assumes  the  content  to  be  equal  to  the  product  of  the  area  of  the 
middle  cross-section  of  the  solid  by  its  length.    This  content  will 
therefore  be  expressed  in  our  symbols  thus  : 

*  *  I  (P  +  P')  x  (q  +  Q'). (4) 

Subtracting  this  from  the  true  content  (1),  we  obtain,  after  a 
little  reduction,  for  the  excess  of  the  former, 

T^UPQ  +  P'Q'-PQ'-P'Q) (5) 

For  the  reasons  before  given  this  may  be  written  thus : 

^  s  I  (p  q  +  p'  g'  -  p  4  -  p'  q) (5') 

Comparing  this  expression  with  (3'),  we  see  that  we  have  merely 
to  reverse  the  deductions  there  established ;  and  that  this  method 
will  give  results  too  small  when  the  preceding  method  gave  them 
too  great,  and  trice  versa. 

The  absolute  error,  however,  will  be  only  half  so  great ;  the  co- 
efficient in  (5')  being  only  one-half  so  great  as  that  in  (3'). 

III.  The  method  of  "  Equivalent  mean  heights"  (or  depths)  is 
now  to  be  examined.     It  consists  (as  is  well  known  to  engineers) 
in  conceiving  the  given  solid  to  be  transformed  in  such  a  way  that 
its  top  surface  shall  be  a  plane,  everywhere  level  cross  ways  at  right 
angles  to  the  length,  and  that  the  areas  of  the  ends  (which  have 
then  become  level  trapezoids)  shall,  at  the  same  time,  be  equivalent 
to  the  original  areas.    The  method  then  assumes  that  the  content 
of  this  new  solid  (which  is  a  true  prismoid)  is  equal  to  the  original 
content  of  the  real  sidelong,  warped-surface-solid. 

This  is  the  method  which  it  has  long  been  customary  to  employ 
when  perfect  accuracy  was  desired ;  and  most  of  the  tables  and 
diagrams  for  sidelong  and  irregular  ground  are  constructed  ou 
this  hypothesis.  The  question  of  its  correctness  is  therefore  an 
important  one. 


APPEXDIX    A. 


37? 


In  Fig.  157,  let  A  B  c  D  be  one  of  the  original   end  areas  or 
cross-sections,  and  let  E  F  c  D  be  an  area  equivalent  to  it,  but 


Fi(T  157 


level  on  top,  if  in  ex- 

cavation,    as    here,  or 

level  at  bottom,  if  in 

embankment.  K  H,  the 

depth     of   this      new 

cross-section,  is  called 

the  "  Equivalent  mean 

depth"  (or  height)  of 

the   original  cross-sec- 

tion.   We  have  first  to  obtain  an  expression  for  it,  in  terms  of 

the  original  side  depths. 

The  investigation  will  be  much  simplified  by  the  same  concep- 
tion as  before,  viz.,  by  producing  the  side  slopes  till  they  meet,  and 
calling,  as  before,  the  new  outside  depths  p  and  Q.  The  height, 
K  L,  of  the  triangle  E  F  L,  is  what  is  now  wanted.  The  area  of 
A  B  L  was  found  on  page  375  to  be  s  p  Q.  Then  the  area  E  F  L 
=  *XKLXEF  =  SKL2,  being  equated  with  s  p  Q,  we  obtain 


The  equivalent  mean  heights  for  the  two  end  areas  will  then  be 
and  /y/p'  q'  ;  and  the  middle  equivalent  mean  height  will  bo 
their  arithmetical  mean.    The  corresponding  middle  area  will  be— 


Using  this  middle  area  and  the  given  end  areas  in  the  pris- 
moidal  rule,  we  obtain,  as  the  content  of  the  solid  by  this  method, 


•    ...    (6) 

Subtracting  this  from  the  true  content  (1),  we  find  the  excess  of 
the  latter  is,  when  reduced, 

isz(V?q'-  yW)2   ......   (7) 

This  expression  is  always  positive,  whatever  the  value  of  P,Q,  p', 
and  Q',  with  a  single  exception,  when  p  q'  =  p'  Q.  Hence  we  have 
arrived  at  this  result:  The  method  of  "equivalent  mean  height*" 
gives  contents  always  less  than  the  true  content  ;  with  one  exception, 


378  APPENDIX  A. 

viz.,  when  the  products  of  the  pairs  of  heights  diagonally  opposite 
to  each  other  are  equal. 

IV.  Some  engineers  have  conceived  the  surface  of  the  ground 
lying  between  two  such  cross-sections  as  we  have  been  discussing, 
lo  be  formed  by  two  triangular  planes  meeting  in  a  line  running 
diagonally  from  p  to  q',  or  from  p'  to  q  (see  Fig.  156),  and  thus 
forming  a  ridge  or  a  hollow  situated  in  this  line.*  But  such  cases 
would  be  abnormal  ones,  and  such  ground  would  not  "  vaiy  uni- 
formly" between  the  cross-sections.  We  will,  however,  examine 
this  conception,  as  it  will  lead  us  to  some  interesting  results. 

We  will  begin  by  supposing  the  solid  to  be  bounded  on  its  sides 
by  vertical  planes  passing  through,  the  outer  side-lines  of  its  sur- 
face, and  to  have  its  base  pass  through  the  line  in  which  the  pro- 
longed side-slopes  would  meet,  so  that  the  heights  of  its  corners 
will  be  P,  Q,  P',  Q',  as  in  the  preceding  discussion. 

Let  now  the  diagonal  be  considered  to  run  from  the  left-hand 
corner  of  the  nearest  end  of  the  solid  to  the  right-hand  corner  of 
the  farther  end  ;  say,  from  the  height  P  to  the  height  Q'.  We  now 
have  to  get  the  middle  area.  The  middle  height  of  the  diagonal 
=  i  (P  +  Q')-  The  middle  width  of  the  left-hand  side  of  the  solid 
—  i  (*  p'  +  *  q1),  and  the  middle  left-hand  height  =  i  (P  +  rO-  The 
middle  left-hand  area  is  therefore— 

i  x  -J  («p'+  SQ')  x  i(p  +  Q'+  P  +  p'). 

Similarly  we  get  the  middle  right-hand  area— 


The  sum  of  these  two  areas  gives  the  complete  middle  area. 
From  it  deduct  the  areas  of  the  triangles  on  each  side  of  the 
original  solid.  The  left-hand  one  has  its  height  =  |  (P  +  P'),  and 
its  base  s  times  that,  and  the  right-hand  one  has  its  height  =  £ 
(Q  +  Q')>  an(i  its  base  *  times  that.  Using  the  middle  area  thus 
obtained,  with  the  end  areas,  in  the  prismoidal  rule,  we  obtain  the 
content  of  the  solid  on  the  new  hypothesis.  Its  expression  may  be 
reduced  to  the  following  : 

i«Z(PQ  +  P'Q'  +  PQ')  ......    (8) 

Subtracting  this  from  the  true  content  (1),  we  get  for  the  excess 
of  the  latter. 
_  ^(P'Q-PQQ  ........     (9) 

*  See  Mr.  J.  B.  Henck's  very  valuable  "  Field  Book  for  Railroad  Engineers," 
page  100. 


APPENDIX    A.  3;  9 

If  we  next  suppose  the  diagonal  to  ran  in  the  other  direction, 
t.  e.,  from  Q  to  P',  we  shall  find  the  excess  of  the  true  content  then 
to  be, 

^(PQ'-P'Q) (10.) 

Hence,  we  infer  that  the  error  on  either  hypothesis  is  numerically 
tlie  same  ;  though  on  one  in  excess  and  on  the  other  in  defect ;  but  that 
the  true  content  is  the  greater  when  the  product  of  the  heights  which  the 
diagonal  joins  is  less  than  the  product  of  the  oilier  two  heights  ;  and 
tike  versa* 

Some  examples  will  show  the  practical  bearings  of  the  principles 
which  have  now  been  established. 

Example  1.  "We  will  begin  with  the  solid  represented  in  Fig.  156. 
It  is  an  exact  excavation  a  hundred  feet  in  length,  all  the  dimen- 
sions being  given  in  feet.  Its  nearer  end  has  the  outside  cuttings, 
p  =  6,  and  q  =  15  ;  and  its  farther  end  has  the  outside  cuttingSj 
p'  =  18,  and  q'  —  12.  The  bottom  width  is  18.  The  side-slopes 
are  1  to  1.  The  areas  of  the  ends  are  279  and  486.  The  middle 
area,  obtained  from  the  mean  cf  the  outside  depths,  is  391.5.  Then 


*  This  admits  of  the  following  geometrical  proof:— 

Let  A  B  c  D  be  the  surface  in  question.  Consider  it  to  be  formed  by  two  tri- 
angular planes,  ABC,  ADC,  meeting 
in  A  c.  Conceive  also  a  vertical 
plane  to  pass  through  A  c,  A'C',  thus 
forming  two  truncated  prisms.  Next 
consider  the  surface  to  be  formed  by 
planes  meeting  in  B  D,  and  conceive 
another  vertical  plane  to  pass  through 
B  D,  B'  D'.  Two  other  truncated  prisms 
are  thus  formed.  Now  conceive  a 
plane  parallel  to  A  B  and  D  c.  It 
will  cut  the  four  planes  of  the 
hypothesis  !n  lines  parallel  to  A  B 
and  D  c,  and  will  thus  form  a 
parallelogram  11'  1"  1'".  The  diagonal  11"  divides  the  lines  AD,  B  c,  pro- 
portionally (as  follows  from  the  similarity  of  the  triangles  formed),  and  la 
therefore  a  generatrix  of  the  warped  surface  which  lies  between  the  two  pairs 
of  plaiies.  But  this  diagonal  of  course  bisects  its  parallelogram ;  the  same  is 
true  of  any  other  generatrix  ;  consequently  the  surface  which  they  form  is  every- 
where midway  between  the  surfaces  of  the  two  pairs  of  truncated  prisms,  and  i* 
therefore  equal  to  half  their  su  n. 


Fig.  15S. 


380  APPENDIX  A. 

tlie  true  content  of  the  solid,  by  the  prismoidal  rule,  is  38,850  cubic 
feet. 

Applying  to  this  example  the  method  of  "  Averaging  end  areas," 
we  get  a  content  of  38,250  cubic  feet,  or  600  cubic  feet  too  little. 
It  is  too  little,  because  the  sum  of  the  products  of  the  depths  diag- 
onally opposite  to  each  other  is  greater  than  the  sum  of  the  products 
of  the  depths  belonging  to  the  same  cross-section.  The  precise 
deficiency  is  given  directly  by  formul&  (3')- 

The  method  of  "  Middle  areas"  gives  39,150  cubic  feet,  or  300 
cubic  feet  too  much ;  in  accordance  with  formula  (5'). 

The  method  of  "  Equivalent  mean  heights"  comes  next.  The 
formula  on  page  377.  gives  the  "  equivalent  mean  heights"  of  the 
two  sections  as  9.97366  and  14.81176  feet.  Their  mean  gives  a 
"  middle  area"  =  376.65.  The  corresponding  content  =  38,860 
cubic  feet.  The  deficiency  is  990  cubic  feet  The  same  is  given 
in  advance  by  formula  (7) ;  since  we  have  (adding  6-v-2*  =  18-*-2 
=  9  to  the  original  depths),  p  =  15,  q  =  24,  p'=  27,  and  Q'=  21 ; 
whence, 

i  x  1  x  100  (^/15  x  21  -  V27  x  24)2=  990. 

The  method  of  imaginary  "  Diagonals"  gives  33,300  cubic  feet, 
if  we  suppose  the  diagonal  to  run  from  p  to  q';  i.  e.,  from  6  to  12, 
thus  forming  a  hollow ;  or  44,400  cubic  feet,  if  it  runs  from  p'  to  q  ; 
i.  e.,  from  15  to  18,  thus  forming  a  ridge.  The  deficiency  in  the 
former  case  is  5550  cubic  feet ;  and  the  excess  in  the  latter  case  is 
the  same  ;  conformably  to  formulas  (9)  and  (10). 

Example  2.  Conceive  the  outside  depths  of  the  farther  end  of 
this  solid  to  be  interchanged,  so  that  12  may  be  on  the  left,  and  18 
on  the  right.  The  true  content  will  then  be  37,950  cubic  feet. 

But  "  Averaging  end  areas"  still  gives  the  same  as  before,  viz., 
38,250  cubic  feet.  It  was  less  than  the  true  content  in  the  former 
case,  but  it  is  now  more,  in  accordance  with  formula  (3').  The 
"  Middle  area"  method  gives  37,800,  or  too  little,  while  before  it 
gave  too  much;  this  result  being  still  in  accordance  with  for- 
mula (5').  "  Equivalent  mean  heights"  give  the  same  as  before, 
and  therefore  still  too  little. 

Example  3.  Conceive  the  depth  g',  of  the  solid  of  Example  1,  to 
be  changed  from  12  to  15,  all  the  other  dimensions  remaining  the 


APPENDIX   A.  381 

same.  The  new  end  area  is  567,  and  the  true  content  becomes 
42,300  cubic  feet.  But  q  =  q'.  Therefore,  according  to  the  prin- 
ciples established  on  page  378.  the  method  of  "  Averaging  areas" 
should  give  the  same  result,  and  it  does  so.  So  too  •with  the 
method  of  "Middle  areas."  The  method  of  "Equivalent  mean 
heights,"  however,  still  gives  too  little,  because  p  x  Q'  is  not  equal 
to  P'  x  Q.  On  making  the  calculation  (the  equivalent  heights  being 
9.97366  and  13.21475),  we  get  a  content  =  41,600  cubic  feet,  or  700 
cubic  feet  too  little  ;  and  formula  (7)  gives  the  same  result. 

Example  4.  In  another  warped  surface  solid,  let  one  end  area 
have  depths  of  15  on  the  left  and  5  on  the  right,  and  the  other  end 
be  5  on  the  left  and  15  on  the  right.  Let  the  breadth  of  road  bed 
be  20  feet,  and  the  side  slopes  2  to  1.  The  true  content  will  be 
38,333  cubic  feet  The  "  Averaging  method"  gives  35,000  cubic 
feet ;  too  little  by  formula  (3'),  because 

5  x  5  +  15  x  15  >  15  x  5  +  15  x  5. 

The  "  Middle  area"  method  gives  40,000  cubic  feet,  an  error  in 
excess  of  half  the  amount  of  the  preceding  deficiency.  "  Equiv- 
alent mean  heights"  give  35,000  cubic  feet ;  not  enough,  because 
p  x  Q',  or  20  x  20  (adding  20  -H  2  x  2  to  the  given  depths)  is  not 
equal  to  p'  x  Q,  or  20  x  20. 

Example  5.  Reverse  one  of  these  sections  so  that  both  may  be  15 
on  the  left,  and  both  be  5  on  the  right.  The  surface  is  then  a 
plane,  and  the  solid  is  a  prism  with  a  uniform  section  of  3500 
square  feet.  For  this  solid  all  the  methods  give  the  same  content ; 
and  this  is  a  final  corroboration  of  our  formulas.  The  "  Averag- 
ing" method  is  now  correct,  because  p  —  p' ,  each  being  15,  or 
because  q  =  q',  each  being  5.  The  "  Middle  area"  method  is  correct 
for  the  same  reason.  The  method  of  "  Equivalent  mean  heights" 
is  now  correct,  because  now  P  Q  =  p'  Q. 

The  method  of  "  Equivalent  mean  heights"  which  the  preceding 
investigation  most  particularly  affects,  seems  to  have  been  in- 
troduced by  Telford,  and  has  since  been  adopted  without  question 
by  most  writers  (the  present  one  included),  when  perfect  accuracy 
was  desired.  The  difficulty  has  been  the  want  of  any  better 
standard  than  itself  with  which  to  compare  its  results.  But  if  the 
positions  which  the  writer  endeavored  to  establish  in  the  first  part  of 
this  paper  be  accepted  as  correct,  this  method  should  be  at  once  and 


382  APPENDIX  A. 

entirely  abandoned— since  its  errors  are  not  of  the  kind  which 
balance  each  other  in  the  long  run,  but  are  always  on  the  same 
side— since  they  are  committed  too  with  a  belief  of  its  perfect  ac- 
curacy, and  therefore  in  the  most  important  and  delicate  cases — 
and  since  they  may  sometimes  be  of  serious  moment,  the  deficiency 
of  the  first  example  given  being  more  than  2£  per  cent,  of  the 
whole  amount ;  no  trifling  item  in  a  class  of  work  which  on  some 
railroads  is  counted  by  millions  of  yards. 

CASE  III. — "  Three  level"  ground. 

This  is  ground  wl.ose  surface  is  such  as  maybe  fairly  represented 
by  the  centre  "  level"  and  the  outside  "  levels,"  i.  e.,  heights  or  depths 
taken  on  the  centre  line,  and  at  the  "  outside  cuttings"  or  "  fillings," 
which  are  the  tops,  or  bottoms,  of  each  side  slope. 

The  areas  are  obtained  by  dividing  them  into  triangles.  See 
Figs.  160  and  164. 

A  common  mode  of  calculating  is  that  of  "  cross  averaging," 
i.  e.,  taking  one-fourth  the  sum  of  the  outside  heights  and  twice  the 
middle  one,  and  using  the  average  as  if  it  were  the  height  of  a  level 
trapezoidal  section.  The  areas  thus  obtained  are  always  too  great. 
For  Fig.  160  it  gives  74.82  instead  of  74.64. 

The  "  Equivalent  mean  height"  is  often  used,  and  there  are 
tables  for  this,  but  this  always  gives  too  small  a  content. 

The  true  content  is  given  by  the  Pnsnunaal  Rule.     See  page  359. 

The  height  of  the  ground  above  the  grade  line  of  the  road  on  the 
centre  line  is  called  the  "  centre  cutting ;"  and  the  heights  at  the 
intersection  of  the  side-slopes  of  the  cuttings  with  the  ground  oc 
each  side  of  any  station  are  called  the  "right  cutting"  and  "  left 
cutting ;"  abbreviated  into  C.  C R.  C L.  C. 

In  embankments,  the  corresponding  heights  are  called  "  centre 

bank,"  "right  bank,"  and  "  left  bank;"  usually  written  C.  B 

R.  B L.  B. 

For  greater  accuracy,  these  cross-sections  should  be  taken  at 
every  chain  or  less.  If  an  abrupt  change  in  the  level  of  the  ground 
requires  a  levelling  between  these  regular  stations,  it  is  called  an 
"  intermediate"  one. 

The  following  table  presents  various  examples  of  irregular  cross 


APPENDIX 


383 


Motions.     The  slopes  are  assumed  to  be  2  to  1,  and  the  width  of 
the  road  to  be  20  feet. 


Station. 

Distance 

L.  C. 

c.  c 

R.C. 

L.  B. 

C.B. 

R.B 

End  Areas 
Excavation. 

End  Areas 
Embankment. 

1 

0 

0 

0 

0 

2 

100 

2.0 

2.0 

2.0 

48. 

3 

100 

3.0 

2.6 

3.4 

74.64 

4 

100 

3.0 

2.0 

62. 

Inter. 

60 

1.0 

0 

0 

0 

0 

0 

5. 

0 

5 

40 

0 

0 

0 

0 

0 

2.0 

0 

10. 

6 

100 

3.0 

4.0 

6.0 

121. 

7 

100 

0 

0 

0 

0 

We  will  proceed  to  sketch  and  note  each  cross-section,  writing 
each  height  vertically  in  its  appropriate  place,  and  show  how  its 
area  is  obtained  by  dividing  it  into  triangles,  of  which  the  base  and 
height  are  known. 

At  station  1  the  cutting  begins,  with  an  area  =  0. 
Fig.  159. 


4.         X  20.  X        4. 

At  station  2,  Fig.  159,  the  section  is  of  uniform  depth,  and  its  area 
IS  bimply  (20  -f  2  X  2)  X  2.0  =  48. 
Fig- 160. 


10. 


10.     X 


6.8 


At  station  3,  Fig.  160,  the  lower  left-hand  triangle  = =  15. 


The  lower  right-hand  triangle  = 
The  two  remaining  triangles  — 


10  X  3.4 


=  17. 


The  entire  area  therefore 
-     24 


: 74.64 


X  20  X       4. 

At  station  4,  only  two  levels  were  thought  necessary,  viz.  those 
of  the  outside  cuttings,  without  the  centre  one.  To  find  the  area, 
consider  the  figure  as  a  trapezoid,  minus  the  right-angled  triangles 
at  each  end. 


Trapezoid  =  (6  +  20  +  4)  X 


=      75. 


Left-hand  triangle 
Right-hand  triangle 


2 
4X2 


—13. 

—  13        

Area  of  cross-section,     -     -     -    62. 

A  simple  algebraic  expression  for  this  area  may  be  found  thus : 
call  the  breadth'of  base  b,  the  outside  cuttings  d  and  e,  the  ratio  of 
side-slopes  to  unity  s.  The  area  will  be 

(b  +  sd  +  se)  (d  +  e)         set*       se*  ,  d  +  e     ,      , 

2  ~  ~2 2~=       ~2 

The  above  example  would  then  be20x|-f2X3X2=50  + 
19  —  62. 

Fig.  162.  * 


10.  X  10. 

Between  stations  4  and  5,  at  60  feet  from  the  former,  an  interme- 
diate cross-section  was  made  necessary,  by  the  cutting  "  running 
out"  on  one  side.  The  area,  Fig.  152,  is  only  the  single  triangle 
10X1.0 

^~r~ 

At  station  5,  40  feet  farther,  the  cutting  entirely  runs  out,  and  its 
*iea  at  that  point  becomes  0.  The  embankment  had  commenced 


APPENDIX   A. 


385 


with  area  0  at  the  preceding  intermediate  station,  and  at  this  sta- 
tion its  area,  Fig.  153,  is =  10. 

At  station  6,  the  cross-section  resembles  that  at  station  3,  in« 

Fig.  164. 
6        X        10.  X        10.        X  12. 

r 

L 
a 


verted,   and   is  calculated   in   the  same  manner  by  division  into 
triangles,  as  is  shown  in  Fig.  154. 

10  X  3 

Left-hand  triangle 


Right-hand  triangle      -     = 
Two  remaining  triangles 


2 
IPX  6 

2 
4  X  (6+  10  + 


=    15. 

=    30 
=    76. 


Entire  area,  =  121. 

At  station  7,  the  embankment  runs  out,  and  the  area  =  0. 


MEAN    HEIGHTS. 

To  apply  the  prismoidal  formula  to  cases  of  irregular  cross-sec- 
tions,  it  is  necessary  to  calculate  the  mean  heights  of  these  cross- 
sections,  to  be  subsequently  averaged  together  to  find  the  middle 
height,  which  produces  the  middle  area.  The  following  problem  is 
therefore  to  be  solved  :  Given  the  area  of  any  irregular  section,  re- 
quired the  mean  height  which  would  produce  the  same  area,  the 
base  and  slopes  remaining  the  same. 


APPENDIX  A. 


Fig.  165. 
b 


X         »* 


Let  a  represent  the  given  area  ;  b  the  breadth  of  base  or  road- 
bed ;  s,  the  ratio  of  side-slopes  to  unity  ;  and  x  the  mean  heighi 
required. 

Then  a  =  sx*  +  bx ;  by  solving  which  equation  we  obtain 


In  all  the  preceding  examples,  —  = 


=  5. 


At  station  3,  (p.  365)  a  =  74.6  .-.  x  =  J  ( — 


v  62.3  —  5  =  7.89  —  5  =  2.89.  If  this  mean  height  be  verified,  it 
will  be  found  to  produce  the  original  area.  Thus  substituting  it  in  the 
above  expression  for  a,  we  obtain  2  X  2.89"+  20  X  2.89=  74.6. 

A  similar  process  will  give  the  mean  heights  for  the  remaining 
i'1-oss-sections.  They  may  then  be  employed,- as  were  the  uniform 
heights  in  the  original  examples,  to  find  the  middle  heights,  and 
thence  the  middle  areas  required  by  the  prismoidal  formula;  or 
as  the  values  of  g  and  h  in  the  easier  formulae,  which  have  been 
therefrom  deduced. 

In  most  cases,  it  will  be  sufficiently  accurate  to  take  only  three 
levels,  viz.,  at  the  centre,  and  at  the  foot,  or  top,  of  each  side  slope. 
The  "  Equivalent  mean  height"  can  be  then  obtained  directly  by  a  re- 
markably simple  expression,  without  previously  calculating  the 
area.  Let  c  =  the  cut  or  fill  at  the  centre,  and  p  and  q  the  outside 
cuttings  or  fillings.  Find  the  expression  for  the  area,  and  put  it 
equal  to  sx2+bx,  as  above,  and  the  following  expression  will  be 
obtained  for  the  value  of  the  mean  height: 


B!  ,•  2s 

When  the  "  distances  out"  are  given,  calling  them  d  and  d',  the 
above  expression  becomes 


,-t/£± 


d' )  (b  +  2  s  c)  -  b. 


APPENBIX  A.  387 


CASE  IV. — Irregular  ground. 

This  is  ground,  such  that  its  cross-section  requires  n,ore  than 
three  heights  to  be  taken  in  order  to  represent  its  transverse  pro- 
file correctly. 

Usually,  the  area  of  such  a  cross-section  is  considered  to  be  di- 
vided into  triangles,  whose  bases  and  perpendiculars  are  known, 
and  are  always  horizontal  and  vertical,  and  the  sum  of  their  areas 
gives  that  of  the  whole  cross-section. 

The  triangles  are  usually  taken  in  pairs,  as  far  as  possible,  the 
vertical  heights  being  taken  as  the  bases,  and  the  horizontal  dis- 
tances as  the  perpendiculars.  The  sum  of  the  products  are  divided 
by  2  instead  of  dividing  each  product  separately. 

For  example,  in  Fig.  166,  commencing  on  the  left,  the  small  tri- 
angle has  5  for  a  base  and  4  for  a  perpendicular.  The  next  verti- 
cal, 5.4  is  a  common  base  for  the  triangles  whose  perpendiculars 
are  13  and  6.  The  next  pair  has  a  common  base  of  8.3,  and  the 
sum  of  the  perpendiculars  is  16.  So  on  for  the  whole  cross-section. 


Fig.  166. 


5x4=  20.0 
5.4  x  19  =  102  6 
8.3  x  16  =  132.8 
3.0  x  22  =  66.0 
6.2  x  19  =  117.8 
3.2  x  21  =  67.2 
6.0  x  2  ss  12.0 


These  end  areas  are  then  USUALLY  averaged  to  get  the  content 

of  the  mass  between  them.    The  correct  method  is  given  on  p.  358 

Sometimes  it  is  impossible  to  take  the  second  set  of  levels  (those 


'388 

on  the  finished  work)  exactly  over,  or  under,  the  first  set  Then 
find  the  area  of  such  cross-sections  above  some  common  datum 
and  take  their  difference.  The  corresponding  levels  might  be  found 
by  proportion. 

When  the  ground  is  very  irregular  and  great  accuracy  is  re- 
quired, its  surface  may  be  divided  into  rectangles  or  squares,  and 
levels  taken  at  each  corner  of  the'se  before  the  cutting  or  filling  is 
'made.  The  original  base  lines  are  axes  of  ordinates,  and  are  care- 
fully preserved.  After  the  work  has  been  done,  levels  are  again 
taken  at  the  same  points.  Then  the  difference  of  the  two  sets  of 
levels,  taken  at  these  points,  will  be  the  depth  of  the  cutting,  or 
height  of  the  filling.  The  content  can  then  be  calculated,  either  by 
combining  the  successive  cross-sections,  or  by  the  method  of  trun- 
cated prisms. 

When  the  ground  is  very  irregular  in  plan  and  in  heights,  as 
in  the  case  of  foundation  pits,  etc.,  the  method  of  cross-sections 
cannot  be  conveniently  or  completely  applied.  Then  the  mass  of 
earth  which  is  to  be  removed  (or  added)  must  be  conceived  to  be 
divided  by  various  vertical  planes  into  prisms  generally  truncated, 
or  pyramids,  and  calculated  by  the  familiar  rules  of  mensuration. 

^si-^.  i'f-..-.  ^^'"^~^L- 

CASE  V. — Excavation  and  Embankment  on  Curves. 

Since  the  distances  are  measured  along  the  centre  line  of  a  road, 
on  curves  as  well  as  on  straight  lines,  the  calculation  of  the  con- 
tents will  not  be  correct  when  the  ground  is  not  level  transversely. 
When  the  cross- sections  are  taken  at  right  angles  to  the  chords  of 
the  curves,  as  is  usual,  the  content  will  be  too  great  on  the  concave 
side  of  the  curve,  and  too  little  on  the  convex  side.  The  two  bal- 
ance each  other  only  on  level  ground. 

If  the  sections  be  measured  at  right  angles  to  the  tangents  at  the 
points  where  they  are  taken,  the  results  will  be  more  nearly  cor- 
rect. 

The  theorem  of  Guldinus  applies  here,  t. e.,  "  The  content  of  any 
body  of  revolution  equals  its  generating  cross-section,  multiplied 
by  the  length  of  the  path  passed  over  by  its  centre  of  gravity." 

The  following  formula  for  the  correction,  in  excavation  on 
curves,  is  from  Henck's  Field  Book,  Art  130 : 


APPENDIX  A.  389 

Let  eat  centre  height,  h— greatest  side  height,  /*'=  least  side 
height,  d  =  greatest  distance  out,  d'  =  least  distance  out,  b  = 
breadth  of  road-bed,  and  R  =  radius  of  curve,  to  find  the  correc- 
tion, C. 


This  correction  is  to  be  added  when  the  highest  ground  is  on 
the  convex  side  of  the  curve,  and  subtracted  when  the  highest 
ground  is  on  the  concave  side. 

TABLES 

FOR    CALCCLATING    EXCAVATION    AND    EMBANKMENT. 

The  TABLES  at  the  end  of  this  volume  are  extracted  from  those 
of  Sir  John  Macneill,  referred  to  on  page  358.  The  numerals  at 
the  top  and  side  of  each  table  represent  the  depths  or  heights  of 
the  cutting  or  filling  at  its  ends.  The  numbers  in  the  body  of  the 
table  indicate  the  number  of  cubic  yards  for  the  corresponding 
depths,  and  for  a  longitudinal  distance  of  1  foot.  Thus,  if  the 
slopes  of  a  given  cutting  be  1£  to  1,  the  base  20  feet,  the  depths  at 
the  two  ends  2  and  5  feet,  and  the  distance  between  them  100  feet, 
find  in  TABLE  1.  the  numeral  2  in  the  side  column  ;  follow  out  the 
horizontal  line  corresponding  to  it  till  it  meets  the  vertical  column 
under  the  numeral  5  in  the  top  line.  At  the  intersection  is  3.31, 
the  cubic  yards  for  a  distance  of  1  foov.  Multiply  this  by  100,  and 
the  product  is  the  number  of  cubic  yards  required. 

The  use  of  such  Tables  is  limited  by  the  inconvenience  of 
making  them  voluminous  enough  to  embrace  every  variety  of  slope, 
base,  and  depths,  (though  the  fractional  numbers  wanting  may  be 
interpolated)  but  in  the  cases  to  which  they  apply,  they  unite  the 
Advantages  of  greatly  lessened  labor,  and  increased  accuracy. 

If  much  work  is  to  be  done  for  any  base  and  side  slope,  not 
found  in  the  tables,  labor  is  saved  and  accuracy  increased  by 
calculating  one  for  them. 


APPENDIX  B. 


- 

STiT  APPENDIX  B. 

no  '.I  bmnTia  t^ii-hl  .^'.i  r.-.-dv/  i'.r^-.'i  ad  oj 


LOCATION    OF    KOAJ>8. 

1.  Planning  the  Route. 

THE  true  bearing  or  azimuth  of  one  place  from  another,  when 
the  latitude  and  longitude  of  each  are  given,  can  be  found  by 
spherical  trigonometry.  But  if  the  two  places  be  veiy  distant,  the 
"  rhumb"  or  loxodromic  line  between  them,  i.  e.  ,  the  line  having 
the  same  bearing  throughout  its  length,  will  not  be  the  shortest 
distance.  The  arc  of  the  great  circle  passing  through  the  points 
must  then  be  adopted.  Its  bearing,  i.  e.,  the  angle  which  it  makes 
with  the  meridians  which  it  crosses,  will  be  constantly  changing. 
Thus,  if  one  point  be  due  west  from  another,  the  east  and  west 
line,  *.  e.,  the  parallel  connecting  them,  is  not  the  shortest  line  be- 
tween them.  For  example,  calling  San  Francisco  due  west  from 
St.  Louis,  the  shortest  line  between  them  by  an  arc  of  a  great  circle 
is  about  9  miles  shorter  than  the  due  west  line  following  the  par- 
allel of  latitude,  and  runs  about  70  miles  north  of  this  parallel. 
A  similar  difference  exists  for  every  other  line  except  a  due  north 
and  south  line. 

For  these  reasons,  in  planning  a  long  route,  the  position  of  points, 
situated  on  the  arc  of  a  great  circle  connecting  the  extremities, 
should  be  determined  in  advance  by  calculating  their  latitude  and 
longitude.  It  would  usually  be  impossible  to  follow  this  line  per- 
fectly, but  it  should  be  approximated  to  as  far  as  possible,  as  is 
done  for  a  straight  line  for  short  distances,  as  on  page  82. 

Other  considerations  cause  the  line  of  a  railroad  to  deviate 
from  the  shortest  line,  as  in  common  roads,  in  order  to  obtain  good 
grades,  moderate  cuttings  and  fillings,  and  to  pass  through  certain 
ruling  points  on  the  line. 


APPENDIX  B.  091 

It  is  usually  best  to  follow  the  valleys  of  the  water-courses  lying 
nearest  in  the  direction  of  the  required  line,  and  in  passing  from 
one  valley  to  another  to  select  that  pass  which  can  be  reached  by 
the  most  uniform  grade. 

2.  Reconnaissance  and  Preliminary  Suwey. 

For  long  distances  this  may  be  executed  by  determining  the  lati- 
tude and  longitude  of  the  ruling  points  with  a  sextant  and  chrono- 
meter, and  determining  the  heights  by  a  barometer. 

For  shorter  distances  the  reconnoissance  is  conducted  as  explained 
on  pp.  81  to  86,  for  common  roads.  More  care,  however,  is  neces- 
sary, owing  to  the  greater  expense  in  building,  sustaining,  and 
working  a  railroad.  In  the  preliminary  survey  of  the  London  and 
Birmingham  Railroad,  Robert  Stephenson  walked  over  the  ground 
twenty  times — a  distance  of  one  hundred  and  twelve  miles. 

3.  Survey  and  Location. 

The  transit  party  usually  goes  ahead,  and  consists  of  a  chief,  a 
transitman,  two  flagmen,  two  chainmen,  and  one  or  more  axmen, 
according  to  the  country. 

The  line  is  marked  out  by  the  transit  party,  by  placing  a  small 
peg  in  the  line  at  every  hundred  feet.  These  pegs  are  driven  so 
that  their  tops  are  nearly  to  the  surface  of  the  ground,  and  then 
large  stakes  are  driven  near  them,  to  aid  in  finding  the  former  in 
retracing  the  line.  The  number  of  the  station  is  marked  on  the 
large  stake  with  red  chalk.  Sometimes  the  larger  stakes  are  placed 
in  the  line,  and  the  small  "  level  pegs"  are  only  driven  at  eveiy 
five  hundred  feet. 

"  Reference  points"  are  also  located  along  the  line  at  important 
points,  so  that  if  the  stakes  in  the  line  be  lost,  the  exact  point  can 
be  found  again. 

Let  o  be  the  point  whose  position  it  is  desired  to  F'g-  107. 
fix.  Select  four  points  as,  A,  B,  c,  and  D  (as  per- 
manent as  possible),  in  such  positions  that  the  lines 
A  B  and  c  D  will  intersect  at  o.  Now  if  the  stake 
nt  o  be  lost,  it  can  be  replaced  by  finding  the  inter- 
section of  the  two  lines.  The  reference  points, 
A,  B,  c,  and  D,  should  be  at  such  distances  from  the 


line  as  not  to  be  disturbed  in  building  the  road.  Any  of  the 
methods  for  determining  the  position  of  a  point  can  be  used  ;  as, 
rectangular,  angular,  or  polar  co-ordinates,  but  the  one  here  given 
is  generally  used. 

The  number  and  size  of  the  openings  (drains  or  culverts)  required 
to  .pass  the  water-courses  under  the  road  should  be  carefully  noted 
and  abundant  room  given  ;  also  the  length  and  height  of  bridges. 

The  geological  formation  of  the  country  should  be  examined, 
the  nature  of  the  surface  noted,  and  generally  everything  which 
can  affect  the  cost  of  the  construction  and  maintenance  of  the 
road. 

A  common  form  for  the  "  Transit  Notes"  is  the  following  :  the 
left-hand  page  is  ruled  into  five  columns,  which  are  headed  as 
follows  : 


Station. 


In  the  first  column  is  placed  the  number  of  the  station  ;  in  the 
second,  the  deflection  of  each  tangent  from  the  preceding  oue  ;  in 
the  third,  the  degree  of  the  curve  connecting  the  tangents;  in  the 
fourth,  the  bearing  of  each  tangent  ;  and  in  the  fifth,  memoranda 
of  the  things  spoken  of  in  the  preceding  paragraph. 

On  the  right-hand  page  of  the  Transit  Field  Book,  plot  the  line 
approximately  in  the  field,  and  on  it  sketch  the  topography,  the 
hills,  valleys,  and  water-courses,  as  nearly  as  possible  in  their  true 
places.*  This  page  should  be  ruled  in  squares. 

The  notes  should  be  commenced  at  the  bottom  of  each  page, 
so  that  when  holding  the  book  in  the  hand  and  looking  along  the 
line,  the  line  in  the  book  will  have  the  same  direction  as  the  one 
on  the  ground. 

The  "  leveller"  follows  the  transit  party,  and  takes  the  heights 
of  the  small  pegs  which  they  have  set  He  is  assisted  by  a  "  rod- 
man."  "Cross-levels"  are  also  taken,  to  a  greater  or  less  width, 
according  to  the  ground,  in  order  to  determine  what  will  be  the 


*  On  sketching  groand  by  various  methods,  see  "  Qill»»pie'8  Levelling, 
Topography,  and  Higher  Surveying."    Part  IV. 


APPENDIX  B.  393 

effect,  in  the  cuttings  and  fillings,  of  moving  the  line  to  the  right 
or  the  left  in  order  to  improve  its  grade  or  curvature. 

The  most  perfect  preliminary  location  of  a  line  would  be  made 
by  first  making  a  topographical  survey,  and  getting  contour  lines 
over  all  the  surface  near  the  proposed  line.  This  can  be  done 
very  rapidly  with  a  level  provided  with  extra  "  stadia  hairs." 

Preliminary  surveys  being  completed,  plots  and  profiles  are 
made ;  curves  put  in  so  as  to  obtain  the  line  of  easiest  curvature  ; 
a  grade  line  put  on  the  profile  so  as  to  nearly  equalize  the  cutting 
«id  filling,  and  at  the  same  time  get  easy  grades.  (See  p.  154.) 

Approximate  grade  contour  lines  may  be  obtained  from  the 
cross-sections  thus :  Knowing  at  each  station  the  relative  heights 
of  the  ground,  find  where  a  horizontal  line,  passing  through  the 
grade  point  at  each  station,  perpendicular  to  the  line  of  the  road, 
would  intersect  the  surface  of  the  ground. 

This  is  most  easily  done,  if  the  slope  is  taken  in  degrees,  by  a 
traverse  table.  Opening  the  table  to  the  degree  of  the  slope,  call- 
ing the  depth  of  the  cut  or  fill  the  departure,  aud  finding  the  lati- 
tude corresponding  to  it,  which  will  be  the  distance  of  the  required 
intersection  to  the  right  or  left.  Mark  on  the  plot  the  places  of 
these  points  of  intersection,  and  draw  a  line  through  these.  This 
will  be  a  line  on  which  there  will  be  no  cutting  or  filling,  and  may 
be  called  a  grade  contour  line. 

The  located  line  should  approach  this  as  nearly  as  other  con- 
sidtratious  (curvatures,  etc.)  will  allow.  It  should  be  a  compromise 
between  this  line  and  the  straight  line. 

Grades  in  railroads  should  be  grouped  by  bringing  the  steep  ones 
together  and  obtaining  some  uniformity  of  them  over  such  a 
length  of  road  as  would  be  worked  by  the  same  engine ;  because 
no  one  engine  can  advantageously  work  easy  grades  and  steep 
ones. 

4     Comparison  of  Lines. 

The  various  lines  which  have   been  surveyed  and  estimated, 
between  two  termini,  are  now  to  be  "  equated."    One  line  may  be 
straight,  but  have  mauy  grades ;    another  level,  but  have  sharp 
curves,  or  be  longer  than  the  former ;  and  so  on. 
17* 


394 


APPENDIX   B. 


In  order  to  ascertain  the  most  economical  line,  we  must  deter- 
mine what  additional  distances  the  curves  or  grades  are  equivalent 
to. 

Then  the  sum  of  these  distances  being  added  to  the  measured 
distance  of  the  several  lines  will  give  their  equated  lengths.  These 
are  to  be  used  in  calculating  the  cost  of  working  the  road  and  the 
additional  capital  to  which  this  is  equivalent. 

In  the  following  example,  to  equate  for  grades,  we  will  call  each 
24'  ascent  equivalent  to  1  mile  additional  in  length,  and  will  con- 
sider 1000°  of  curvature  equivalent  to  1  mile  of  distance.  To 
obtain  the  data  for  the  later,  the  length  of  each  curve  in  chains 
is  multiplied  by  the  degree  of  the  curve,  and  the  sum  of  all  these 
products  gives  the  total  curvature  of  the  line.  Thus : 


No.  .of 
curve. 

Radius. 

Degree. 

Length. 

Total 
curvature. 

1 

1146 

5° 

1000 

50* 

2 

5730 

1° 

4600 

46° 

Example. — Line  A  has  5  miles  24'  grade,  6  miles  12'  grade,  and 
total  curvature  =  4000°.  Line  B  has  10  miles  48'  grade,  10  miles  24' 
grade,  and  total  curvature  =  1000°.  The  expenses  of  maintaining 
the  road  varies  with  the  travel  on  it  Call  it  $1000  annually  per 
nile  of  actual  length,  and  find  the  equivalent  capital  at  6  per  cent. 
The  expense  of  working  also  varies  with  the  trafic.  It  is  pro- 
portional to  the  equated  length.  We  will  call  it  $2000  per  mile  of 
this.  Find  its  equivalent  capital.  The  last  column  Is  the  sum 
of  the  three  preceding  columns. 


Name 
of 
Line. 

Meas- 
ured 
Length. 

Equat- 
ed 
Length. 

Estimated 
cost  of 
construction 

Capital  for 
maintaining. 

Capital  for 
Working. 

Total 
Capital.] 

A. 

100 

112 

$4000000 

1666666.66 

3733333.33 

9400000.01 

B. 

90 

121 

$3800000 

1500000.00 

4033333.33 

9333333.33 

APPENDIX   B..  395 

Final  Location.— The  best  line  having  been  chosen,  it  is  then  to 
be  staked  out  For  grade  book,  see  p.  146.  Its  columns  3,  4,  5, 
and  6  may  be  omitted.  The  side  stakes  for  construction  are  set  as 
on  page  457.  The  estimates  are  made  as  for  common  roads,  with 
the  addition  of  the  new  items  of  rails,  ties,  etc.,  etc.' 


39B  APPENDIX 


APPENDIX    0. 

;,wfe  ,,s.*o  ,t:O  .sMci  1o  ?rao 

KAILKOAD  CUBVK8. 

A  RAILROAD  curve  is  a  portion  of  the  road  curved  horizontally, 
BO  as  to  form  an  arc,  usually  circular,  terminating  at  each  end  in 
straight  portions  which  are  tangent  to  it 

A  railroad  curve  is  "determined"  when  its  starting  point,  its 
radius,  and  its  length  are  known.  When  these  have  been  obtained, 
points  in  the  curve  can  be  fixed  in  various  ways.  Such  points  are 
angles  of  a  polygon  whose  sides  are  chords  of  the  desired  arcs,  and 
approximately  coincide  with  them. 

Usually  these  chords  are  chains  of  one  hundred  feet,  and  the 
angle  in  degrees  which  each  one  subtends  at  the  centre,  is  called 
the  "  degree"  of  the  curve.  It  equals  the  angle  of  deflection  of  each 
of  these  chords  from  the  preceding  one.  The  relation  between 
this  angle  and  the  radius  is  important. 

Approximately,  and  sufficiently  near  for  the  usual  curves,  the 
angle  of  deflection  in  degrees  =  5730  -j-  radius  in  feet 

Precisely  :  Sine  of  half  the  degree  =  —  chord  —  ^ 
twice  radius 

The  subject  is  divided  into  two  parts  :— 

PART  I. 

GENERAL  PROBLEMS  ON  CURVES  ;  or  how  to  determine  a  curve 
so  that  it  shall  fulfill  certain  conditions,  e.  g., 
A.  To  unite  two  given  tangents. 
JR.  To  start  from  a  given  tangent  and  pass  through  a  given 

point. 
(7.  To  unite  a  given  tangent  line  and  a  given  curve,  etc.,  etc. 

PART  II. 

METHODS  OF  RUNNING  CURVES  WHEN  DETERMINED;  f.  «., 
methods  for  fixing  points  in  them  ;  and  transformations  of  the  for- 
mulas of  Part  I.  to  suit  these  different  methods. 


APPENDIX   C. 
PART  I. 

GENERAL   PROBLEMS 

CUE  A.— To  UNITE  Vvvo  GIYEN  TANGENT  LINES. 
Ite.  A 


! 


897 


In  all  the  figures  the  starting  point  of  the  curve  is  lettered  At 
and  its  terminus  z.    I  is  the  point  of  intersection  of  the  tangent^ 


398  APPENDIX  C. 

and  D°  is  the  angle  of  deflection  of  one  from  the  other,    o  is  the 
centre  of  the  arc.         gjyjs  ^33 

Its  radius  is  therefore  o  A  =  o  z  =  r.     The  equal  tangents  are, 

AI  =  IZ  :=<. 

^>^'  '  ~" 

PROBLEM  T 

Given  two  intersecting  tangents,  and  also  the  starting  point,  A,  on  one 
of  them,  to  find  radius  and  length  of  curve.  Fig.  1. 

Graphically,  on  a  plot.  Set  off  i  z  =  A  i.  At  A  and  z  draw  per- 
pendiculars to  the  respective  tangents,  and  their  intersection  will 
be  the  centre  required.  It  will  also  be  in  the  line  bisecting  the 
angle,  A  i  z. 

When  the  lines  are  given  on  the  ground.  Set  off  I  z  =  A  i. 
Measure  A  z ;  mark  its  middle  point,  M,  and  measure  i  M.  Then 
from  the  similar  triangles,  AMI  and  A  MO, 

;rjp~i 

Trigonometrically.    When  the  lines  are  given  by  their  angle  of 
deflection,  then  from  the  right-angled  triangle,  o  A  r, 
o  A  =  AI  cot.  i  T  i  z  =  t  cot.  \ D". 

The  length  of  curve  A  z  =  o  A 

PROBLEM  II. 

Given  two  tangents,  and  also  the  desired  radius,  o  A,  to  find  the  start' 
ing  point,  and  length  of  curve. 

Graphically  on  a  plot.  Draw  parallels  to  the  tangents  at  a  dis- 
tance =  radius.  Their  intersection  will  be  the  centre.  1 1  will  also 
be  in  the  line  bisecting  the  angle  I.  T  Fig.  3 

fir  calculation,  when  the  lines 
are  given  on  the  ground,  Fig.  2, 
measure  equal  distances  from  I  to 
p  and  Q.  Measure  P  Q ;  mark  its 
middle  point,  s,  and  measure  si. 
Then  from  the  similar  triangles, 
A  o  i  and  FBI, 


APPENDIX   C. 


399 


Otherwise,  by  trial,  Fig.  3  Run  from  a  random  point,  A',  till  the 
tangent  at  the  end  of  the  Pig.  3. 

curve  is  parallel  to  second 
tangent,  I  z,  as  XT  v  at  v. 
Measure  v  z  parallel  to 
first  tangent,  A  i;  move 
the  starting  point  that 
distance  and  repeat. 

"When  the  lines  are 
given  by  their  angle  of 
deflection,  we  have, 

i  A  =  o  A  tan.  i  D?.        Length  of  curve  =  r  ^nj- 

PROBLEM  III. 

Given  two  intersecting  tangents,  and  also  the  distance  i  cfrom  tluir 
intersection  to  a  point  through  ichich  tJie  curve  must  pass.  Required 
to  find  the  starting  point,  A,  radius,  r,  and  length  of  curve.  Fig.  1. 

Graphically.  Draw  a  line  bisecting  A  i  z.  Through  c  (at  the 
given  distance  measured  on  the  line)  draw  a  perpendicular  to  it, 
meeting  the  tangents  in  B  and  D.  Set  off  c  B  from  B  to  A,  and  its 
equal  c  D,  from  D  to  z.  Perpendiculars  at  A  and  z  will  intersect  in 
the  centre,  which  will  also  be  in  the  bisecting  line. 

By  calculation.    In  triangle,  ACT, 

sin.  ACT 


sin.  i  A  c  :  sin.  ACl::iC:Ai  = 


-r  -  . 
sin.  i  A  c 


sin.  A  c  i  =  siu.  A  c  o  =  cos.c  A  z  =  cos.i  i  A  z  =  cos.  \  A  o  z  =cos.J  D* 
and, 

sin.  r  A  c  =  sin.  £  A  o  c  =  sin.  £  A  o  z  =  sin.  \  D°. 
Hence, 

cos.  i  D 


To  find  the  radius, 

O  A  =  A  I  COL  A  O  I  =  A  I  COt.  i  D  =  I  C  COt.  £  D  .  COt  i  D°. 

Hence, 

o  A  =  i  c  cot.  ^  D°  cot.  i  D". 
Conversely, 

i  c  =  I  .  tan.  \  D*.     And  i  c  =  r  .  tan.  \  D°  .  tan.  i  D*. 


400 


APPENDIX  t. 


PROBLEM  IV. 


Given  two  intersecting  tangents,  and  also  a  point,  p,  through  which 
the  curve,  must  pass,  to  find  the  starting  point,  A,  radius,  r,  and  length 
of  curve.  Fig.  4. 

Graphically,   on     the   ground.  Kg-  4- 

Bisect  angle  at  i.  Through  p 
draw  a  perpendicular  to  bisect- 
ing line,  intersecting  tangents 
at  H  and  H'.  Construct  a  mean 
proportional  between  H  p  and 
p  H'.  It  equals  H  A,  since  H  A 
=</(HP  x  HP')=\/(HP  x  PH'). 
This  gives  A,  and,  therefore, 
gives  I  A,  and  thence  A  o,  by 
Problem  I. 

On  a  plot.  Draw  the  bisectrix 
of  the  angle,  I.  Join  IP.  Through 
p  draw  a  perpendicular,  M  F,  to 
the  nearest  tangent.  With  M  as 
a  centre  and  MF  as  a  radius, 
describe  an  arc  cutting  i  p  in  B. 
Join  F  B  and  M  B.  Draw  p  o  parallel  to  K  M,  and  P  A  parallel  to 
K  F.  o  will  be  the  required  centre,  and  A  the  starting  point. 

By  calculation.  Measure  or  calculate  the  rectangular  co-ordi- 
nates, i  F  and  F  P,  of  the  given  point.  Then  we  get, 

F  A  =  FP,  COt.  |-D°  ±   y[(FPCOt  |D°  +  I  F)2  —  I  F*  —  FP*] 

I  A  =  i  F  +  FA,  and  o  A  =  i  A  cot.  i  D°. 

Analytically.  Given  angle,  A  i  z,  and  the  point,  p,  by  rectangular 
co-ordinates  from  i,  p  F  and  F  i,  to  find  F  A,  etc. 

A  F  =s  Q  P  =  \/(Q  P*  —  O  Q*)  =  Vl>0*  -  (A  O  -  F  P)*] 

a=  ^(2  A  O,  F  P  —  F  P* > 

By  Prob.  VI.  (or  by  mensuration), 

x  =  >y/(2  ry  —  y*),  or  A  F  =  >y/(2  A  O  x  F  p  —  F  P*). 
By  Prob.  I.    AO  =  AI,  tan.  1  AI  Z  =  (AF  +FI)  tan.  iL 


APPENDIX  C.  401 

Substituting  A  o  in  the  above ; 

A  F  =  -v/[2  F  P  (A  F  +  FI)  tan.  £  r  —  F  p3]. 

AF*  =2FP-,AFtan.  1 1  +  2FF,Fitan.  $i  —  »p*. 

AF*  —  2  F  F,  tan.  i  i,  A  F  =  2  F  P,  F  I,  tan.  i  I  —  F  p*. 

AF  =  FP,tan.ii  ±  /y/(2  F  P,  F  i  tan.  1 1  —  FP*  +F  P*  tan.*|l) 

A  F  =s  F  P,  tan.  i  I  ±  <v/[(p  r»  ten''  i  I  +  F  i)a  —  F  I1—  F  ^1- 

Note  to  Case  A,  Profo.  Z,  ZT,  ZZZ,  an<Z  JFI 

When  the  intersection,  I,  of  the  tangents  is  inaccessible,  D°  and 
t  must  be  calculated.  Fig<  5.  From  A,  run  one  or  more  lines  to  meet 
the  other  tangent  at  some  point,  as  \v.  Then  the  desired  angle 
at  i  is  obtained  by  subtracting  the  sum  of  all  the  interior  angles 


>^ 

rcHc 


from  two  right  angles,  taken  as  many  times,  less  two,  as  the  figure 
has  sides.  When  the  lines  are  run  by  traversing,  the  reading  from 
vr  to  z  at  once  gives  D°.  A  w  is  calculated  by  latitudes  and  de- 
partures. Then  I  A,  in  the  triangle  AI  w  is  calculated  by  trigo- 
nometry. 


402  APPENDIX  C. 

CASE  B.—  To    START    FROM    A  GIVEN   TANGENT  AND    PASS 

THROUGH  A  GIVEN  POINT. 

PROBLEM  V. 

Given  this  tangent  and  point,  z,  to  find  radius,  length  of  tangent, 
and  length  of  curve. 

Graphically  on  a  plot.  At  z  make 
an  angle  A  z  i  =  z  A  i.  Draw  per- 
pendiculars at  A  and  z,  and  their 
intersections  is  the  centre.  Otherwise, 
draw  perpendicular  at  A,  and  make 
angle  A  z  o  =  z  A  O. 

By  calculation.  There  are  two 
sub-cases,  according  to  what  the 
data  are. 

1.  When  the  point  is  given  by  its 
polar  co-ordinates,  as  T  A  z  and  A  z, 

We  have,  r  =  -^£~       ahd  '  =  2Tz' 
Length  of  curve  =  2  r  •    „     • 

An  gular  length  of  curve  =  AOZ°  =  2TAZ. 

Conversely.    Given  radius  and  T  A  z,  to  find  A  z.  A  z  =  2  r  sin.  T  A  z. 

2.  When  the  point  is  given  by  its  rectangular  co-ordinates,  viz., 
A  T  =  x,  and  T  z  =  y. 


Length  of  curve  =  2  r  ^^  ;  tan.  IAZ=  —  =—  . 

Angular  length  of  curve,  AOZ  =  2TAz. 

The  direction  of  the  final  tangent  at  z,  t.  «.,  its  deflection  TIB 
from  the  first  tangent  =  A  oz. 

Note.  —  To  calculate  the  rectangular  co-ordinates  of  a  point  of  a 
curve  from  various  data. 

1.  Given  the  polar  co-ordinates, 

-r  =  AT  =  AZCOS.  TAZ,  y  =  TZ  =AZsin.  TAZ. 

2.  Given  the  angle  of  deflection  of  the  tangents,  and  radius  of 
curve, 

x  =  A  T  =  o  A  sin.  D,^  =  TZ=OA(I  —  cos.  D)  =  2  o  A  (gin.  1  D)1. 


APPENDIX  C.  403 

8.  Given  radius  and  length  of  tangent. 
Find  D°,  having  tangent 

i  A  I  z  =  y;  and  D  =  180°  —  Aiz. 

Then,  x=st(l  +  COS.D'),  and  y  =  t.  sin.  AI  z  =  £.  BUI.  D*. 
4  Given  the  radius  of  curve  and  its  length, 

0      length  of  curve  x  57.3 


Then  apply  the  second  case. 

Finding  the  rectangular  co-ordinates  of  the  end  of  a  curve,  is 
equivalent  to  finding  how  far  the  curve  will  depart  from  its  first 
tangent,  and  what  point  of  that  tangent  its  extremity  will  be  oppo- 
site to. 

PROBLEM  VI. 

Given  this  tangent  and  point,  as  in  Prob.  V.,  and  also  the  radius,  to 
find  the  starting  point,  length  of  tangent,  and  length  of  curve.  (Fig.  6.) 

"When  the  point  is  given  by  polar  co-ordinates,  change  them  to 
rectangular  co-ordinates  by  the  preceding  formulas,  i.  e.,  find  TZ 
and  the  position  of  T. 

Then, 

T  A  =  <y/(2  A  o  x  T  z  —  T  za)  ;  or,  *  =  ^/(2  r  y  —  y*). 
Length  of  i  A  and  of  curve  are  as  in  the  last  problem. 

Conversely.    Given  radius  and  tangent,  to  find  T  z. 
T  z  =  o  A  —  /y/(o  A*  —  A  T2)  ;  or,  y  =  r  —  y^r2  —  «*). 

CASE  C.  —  GIVEN  A  TANGENT  LINE  AND  A  CURVE  ALREADY  BUS. 

PROBLEM  VII. 

Given    the    radius,   r,  and  Fig-  ?• 

length,  I,  of  a  curve  ;  required 
the  radius,  r1,  of  another  curve, 
A  z',  or  A'  z',  which  shall  start 
from  the  same  tangent,  and  pass 
at  a  given  distance,  z  z',  fr&m 
tJie  end  of  the  first  curve. 

Precisely.  Fig.  7.—  Find  the 
rectangular  co-ordinates  of  z, 
arid  then  of  z',  and  then  apply  J 
Problem  V.,  Case  2. 

Conversely.  Given  the  two 
curves,  A  z  and  A  z',  or  A'  z', 


404  APPENDIX  C. 

to  find  the  distance  apart,  z  z'.    When  they  start  from  the  same 
point,  A  ; 


When  they  do  not,  add  A  A'  (with  proper  sign)  to  a/,  and  use  the 
sum  for  x'  in  the  formula  4  x'  and  y"  are  the  co-ordinates  of  z'. 

To  find  the  direction  of  the  distance,  z  z',  f.  e.,  the  angle  z'  z  "W, 
we  have, 

sin.  z'  z  w  =    ~~,   »  and  cos.  z'  z  w  =  — ~?. 
co  (        •    z  z       ...,'^v^  ^  .yv.,V(-».-  .,  z  z 

Reckoning  this  angle  around  from  z  w,  to  the  left,  as  is  usual,  the 
trigonometric  signs  will  determine  the  quadrant  in  which  z  z'  lies, 
and  therefore  its  absolute  direction. 

Approximately.  When  the  curves  are  of  the  same  length,  of  large 
radius,  and  do  not  diverge  far. 

For  the  general  problem.  When  the  curves  start  from  the  same 
point,  A,*  t,  ^ ,  u  ^f).  >i9j  sc  fa  j.  i>;  •«•?; 


A  z"  ±  2  r  z  z' 

using  the  plus  sign  when  the  curve  A  z'  passes  farther  from  the 
tangent  than  does  A  z,  and  vice  versa. 
When  they  start  from  different  points,  A  and  A', 

r>  =  T  (AZ±AA/)' 
A  z*  ±  2  r  z  z' 

Conversely.    Given  the  two  curves  to  find  their  distance  apart 
When  they  start  from  the  same  point,  A, 

zz'=Az*-r-r/ 
When  they  do  not, 

ue-Qt 


2rr" 


PROBLEM  VIIL 

Given  the  radius,  r,  and  the  length,  I,  of  a  curve ;  required  the 
radius,  rf,  of  another  curve,  which  s7iall  start  from  the  same  tangent  at 
A',  and  meet  the  first  curve  at  a  point,  z. 

Precisely.  Find  the  rectangular  co  ordinates  of  z,  and  then 
apply  Protx  V.,  Case  2. 


Approximately. 


APPENDIX  C. 


AZ  ±  A  A 


405 


This  is  from  the  approximation  in  Prob.  VII.,  by  making  z  *  =  0. 

PART  IL 
To  BUN   THE   CuKVEa. 

FIB8T  METHOD. 

By  "  tangential  angles;"  i.  e.t  angles  of  divergence  from  iangentt. 
From  the  starting  point  set  off,  with  a  transit  or  a  compass, 
equal  diverging  angles,  each  subtended  by  equal  chords;  i,  A, 

Fig.  8. 


chains.    After  determining  n  points,  go  to  the  last  one,  sight  back 
to  the  first  one,  and  deflect  from  the  chord,  z  A,  an  angle  equal  to 


406  APPENDIX  C. 

that  already  turned ;  t.  <?.,  i  A  z.  Tou  are  then  pointing  in  the  tan* 
gent  z  I,  which  may  be  prolonged  as  a  tangent,  or  used  to  continue 
the  curve  as  at  first  This  is  the  method  most  commonly  used. 

For  example  ;  let  it  be  required  to  run  a  four-degree  curve  for 
five  stations,  commencing  at  A,  Fig.  8.  Then  the  angle  to  be  turned 
off  each  time  is  two  degrees.  This  is  called  the  "  tangential  aa- 
gle,"  and  is  represented  by  d. 

Set  up  the  transit  at  A,  with  the  telescope  pointing  toward  i. 
Turn  2°  to  the  right,  and  fix  the  point  B  in  the  line  of  sight  at  a 
distance  from  A  of  100  feet  Then  turn  2°  more  to  the  right,  and 
fix  the  point  c  in  the  line  of  sight  at  a  distance  of  100  feet  from  B. 
So  on  for  any  number  of  stations,  turning  2°  each  tune,  and  fixing 
the  station  in  the  line  of  sight  at  a  distance  of  100  feet  from  the 
preceding  one.  To  get  on  the  tangent  at  z,  set  up  the  transit  at 
z,  with  the  telescope  pointing  to  A.  Turn  to  the  right  10°  (the 
number  of  degrees  deflected  from  A  i),  and  the  telescope  will  then 
be  pointing  to  I,  along  the  tangent  I  z.  It  frequently  happens  that 
the  entire  curve  cannot  be  run  from  A.  Suppose  it  is  desired  to  make 
a  changing  point  at  D,set  up  at  D  with  the  telescope  directed  toward 
A.  Turn  to  the  right  6°  (the  whole  number  of  degrees  deflected 
from  the  tangent),  and  the  telescope  will  then  be  pointing  along  the 
tangent  at  D,  and  the  curve  can  be  prolonged  in  the  same  manner 
as  when  starting  at  A. 

When  the  "  tangential  angle"  contains  some  odd  seconds,  keep 
account  of  them,  and  when  they  amount  to  a  minute,  add  it  in. 

When  a  curve  does  not  come  out  just  right,  i,  e.,  to  some  point 
z',  instead  of  z,  some  engineers,  instead  of  running  it  over  until  it 
does,  will  move  z'  to  z,  and  the  other  stakes  a  distance  proportional 
to  the  square  of  their  distance  from  the  starting  point  This  is  a 
tolerable  approximation. 

NOTATION. 

6°  =  "  tangential  angle"  by  which  the  curve  is  run. 
25°  =  "degree"  of  curve  =  the  angle  subtended  at  the  centre 
by  a  chord  of  100'. 

c  =  length  of  one  of  the  equal  chords,  usually  100  feet 
.  n  ss:  number  of  chords  in  the  curve. 
.  r  =  radius  of  the  curve. 


APPENDIX  C.  407 

Chord  and  radius  must  be  in  the  same  unit  of  measure. 
!AZ  =  n5°.    D8  =  AOZ  =  27i  5°  =2iAZ. 


The  length  of  the  curve  in  n  chords  = 


25°          25° 

If  n  have  a.  fraction,  the  curve  will  end  with  a  "  sub-chord"  i.  «. 
a  similar  fraction  of  a  whole  chord. 

FUNDAMENTAL  THEOREMS. 


:  2sin.5°' 


With  hundred  feet  chords,  approximately, 


This  is  near  enough  for  curves  of  large  radius. 
For  any  other  chord,  c',  and  a  corresponding  tangential  angle  9". 

sin.  <5/0=sin.  5°  —  . 

By  this  formula  long  chords  may  be  used  when  more  convenient 
For  slwrt  chords,  approximately, 


A  curve  whose  chords  are  of  an  equal  length,  and  S  has  odd 
minutes  and  seconds,  may  be  run  with  5'"  in  even  minutes,  by 

using  another  chord,  c',  given  by,  c'=  c    •  '  *' 

PROBLEMS. 

The  enunciations  are  as  in  the  "  General  Problems,"  Part  L.only 
substituting  "  Tangential  Angle"  for  "  Radius." 

CASE  A. 
PROBLEM    I. 

Given  two  intersecting  tangents,  and  also  the  starting  point  on  on* 
of  them,  i.  e.,  given  D1  and  t,  to  find  5>  .    (Fig.  1.) 

sin.  S  '  =  c  tap-  i  qit  an(j  angular  length  of  curve  =  2  n  3°. 
21 


408  APPENDIX  C. 


PKOJSLEM  II. 

Given  two  intersecting  tangents,  and  also  the  tangential  angle,  i.  ft, 
given  j>°  and  5°,  to  find  t.    (Fig.  1.) 


PROBLEM  III. 

• 
Given  two  intersecting  tangents,  and  also  the  distance  from  the 

vertex  to  a  point  through  which  the  curve  must  pass,  i.  e.,  given  D°  and 
I  c,  to  find  t  and  d°.    (Fig.  1.) 

sin.  5°  =  c  tan.4D°tan.jD°       d    =  ^    . 

2ic 

tan  i  D°  tan  -Jr  D* 

Conversely,      i  c  =  c  -  -  —  .  —  ^-2  —  ,  and  ic  =  t  tan.  i  D  . 
2  sin.  o 

PKOBLEM  IV. 

Given  two  intersecting  tangents,  and  also  a  point  tJirough  which  ifa 
curve  must  pass,  i.  e.,  given  D°  and  tJie  co-ordinates  ofp,  to  find  5°  and 
A  i.  (Fig.  4.) 

Find  F  A  and  A  i  as  in  General  Problem  IV. 
tan.  i  D°  • 


sin.  5°  =  c 


2AI     ' 


CASE   B.— To   START   FROM  A   GIVEN   TANGENT,    AND    PASB 

THROUGH  A  GIVEN  POINT. 

PROBLEM  V. 

Given  this  tangent  and  point,  and  also  the  starting  point.     (Fig.  6.) 
1.  Given  A  z  and  i  A  z,  to  find  5°  and  i  A. 

8in.  5°  =  c  sin-IAZ.  and  A  i  = ±1— 

A  Z  2  COS.   I  A  Z 


Approximately^  $"  = 


AZ  (in  chains)'' 
Conversely,  A  z  —  c 


APPENDIX   C.  409 


2.  Qiveu  A  T  =  x,  and  T  z  =  y,  to  find  5°  and  A  i. 

of  +  y* 


sin.  2n<5° 
___ 


PROBLEM  VL 

tangent  and  point,  as  in  Problem  V.,  and  also  8°  and 
rz,tofind±T.    (Fig.  6.) 


sin.  5 
Conversely.    Given  6°  and  A  T  to  find  T  z. 

Radius  =-;  then  T  z=y  =  r—  ^(i*  —a?). 


CASE  C. 
PROBLEM  VII. 

Given  8°,  n,  and  z  z',  to  find  8'°.    (Fig.  7.) 
Accurately,  as  in  General  Problem  VII. 
Approximately,  z  z'  being  in  feet, 


8'°  =5°  ±     ~     and  conversely,  z  z/  =  (5°  o>  5'°)      -. 
When  the  curves  start  at  a  distance  apart  =  A  A'  (in  chains), 
,  and  z  »'  =  *[n-  <**> 


PROBLEM  VIIL 

Czwra  (5°,  n,  and  A  A',  to  find  8'".    (Fig.  7.) 
Accurately,  as  in  General  Problem  VIII. 

Approximately,  8'° 


410 


APPENDIX  C. 


SECOND  METHOD. 

By  "  chord  angles"  i.e.,  angles  of  deflection  from  chords.    (Fig.  9.) 
Turn  5°  and  fix  B  as  in  the  first  method.    Set  up  at  B,  and  turn 
25°  from  AB  prolonged,  and  fix  c  at  a  distance  of  100  feet  from  B, 
Fig.  9. 


and  so  go  on  any  number  of  stations,  turning  2  <5°  from  each  chord 
produced.  To  get  into  the  tangent  at  any  point,  turn  5°.  Find 
6°  as  in  the  first  method.  The  defect  of  this  method  is  the  fre- 
quent setting  of  the  instrument 

THIRD  METHOD. 

With  two  transits  and  no  cJiain.    (Fig.  10.) 

Set  the  transits  at  A  and  z.  Turn  the  telescope  of  the  former  to 
t,  and  that  of  the  latter 
to  A.  Then  deflect  equal 
angles  in  the  same  direc- 
tion (to  the  right),  and  set 
stakes  at  the  intersections 
of  the  corresponding  lines 
of  sight.  The  principle 
is  that  the  vertices  of  a 

series    of    eq\ial    angl 

constructed  on  the  same 

chord,  will  all  lie  in  the  arc  of  a  circle.     Given  the  chord,  the 

angle  to  be  turned  is  found  as  in  the  first  method. 


APPENDIX  C.  411 

FOURTH  METHOD. 

With  a  sextant;  reflecting  the  angle  in  a  segment.  (Fig.  1.) 
Given  A  z  and  i  A  z  ;  either  on  the  ground  or  calculated.  Set 
the  sextant  (or  other  reflecting  instrument)  to  the  supplement  ol 
I  A  z.  Move  about  till  poles  at  \  and  z  (seen,  one  by  direct 
vision,  and  the  other  by  reflection)  appear  to  coincide.  Drop  a 
plumb  line  from  the  eye,  and  it  will  fix  one  point  of  the  curve. 
Repeat  this  at  as  many  points  of  the  curve  between  A  and  z  as  are 
desired.  The  principle  is,  that  the  angle  between  the  tangent  and 
chord  at  any  point  of  a  circle  is  equal  to  the  angle  inscribed  in  the 
segment,  and  equal  to  the  supplement  of  the  angle  inscribed  in 
the  original  segment. 

FIFTH  METHOD. 

By  versed  sines.    For  the   method  of  running    the   curve,  see 
pp.  140  and  141.    (Figs.  64  and  65.) 

Let  v  =  versed  sine  D  E, 
c  =  chord  A  E  =  E  F. 


By  Prob.  I.  v  =  ^  -  C—.  -  . 
2  A  i  tan.  t  AIZ 

For  a  sub-chord  c',  the  versed  sine  v'  =vf—  j  . 

Hence,  when  c'  =  %  c,  v'  —  \  v,  and  so  on. 
To  find,  approximately,  intermediate  points, 

E  D  =  A  E  sin.  BAD;  or  v  =  e  sin.  6*. 
Approximately.  v  =  \  5°  and  5°  =  f  v. 

BIXTH  METHOD. 

By  deflection  distances  from  chords  produced,  or  double  versed 
sines.    (Fig.  9.) 
Let  d  represent  one  of  the  deflection  distances,  as  c  B.    Then 


412  APPENDIX  0. 

A  B  is  prolonged  until  B  R  =  A  B.  The  first  station,  B,  is  set  by  a 
"  tangent  deflection,"  F  B,  from  the  tangent,  A  I.  F  B  =  }  B  C ;  t. «., 
a  tangent  deflection  is  half  a  chord  deflection. 

SEVENTH  METHOD. 

By  offsets  from  tangents.    (Fig.  11.) 
Fig.  11. 


1.  Exactly.    Given  radius,  o  A,  and  distance  on  tangent,  A  K,  to 
find  offset  from  tangent,  K  B. 

KB  =  AH  =  r  —  ^/(r*  —  A  KS). 

2.  Approximately. 

A  Ba 

AH  :  AB  ::  AB  :  2OA;  .'.  AH  = . 

£OA 

Calling  A  K  =  A  B  (which  it  is  approximately),  we  have, 
_  AK*    _    tangent3 
~  2  o  A      2  x  radius' 

When  tungent  =  -fa  radius,  the  error  of  the  approximation  is 
.000013  radius  =  nfors  radius. 

When  tangent  =  ^  radius,  error  =  .00051  r  =  5-^5  r. 
"        =i      "         "  0.009  r  =  rh-r. 

Required,  lengtli  of  tangent  which  will  make  the  chords  A  B,  etc., 
even  chains. 

Sin.  |  A  o  B  =  — —    .    AK  =  HB=SOA  sin.  A  o  B. 

2  O  A 

When  the  offsets  become  too  long  to  be  set  off  with  accuracy  or 
ease,  or  when  the  tangent  deviates  from  the  desired  curve  so  fai 


APPENDIX   C. 


413 


as  to  fall  on  impracticable  ground,  "  auxiliary  tangents"  may  be 
usec!. 

From  A  points  have  been  fixed  to  B.  A  new  tangent  at  B  is  de- 
sired. From  A  set  off  a  distance,  A  c,  to  be  calculated  by  a  formula 
given  below,  c  B  produced  is  the  desired  new  tangent.  Set  off 
from  it  offsets  as  before.  If  the  ground  prevents  A  c  being  set  off, 
set  off  A  o,  and  produce  a  B  as  before. 

To  get  a  new  tangent  at  D,  set  off  B  E  =  A  c,  and  E  D  produced 
is  the  third  tangent  required. 

Or,  set  off  K  E  on  first  tangent  prolonged,  and  prolong  E  D  aa 
before.  So  on  for  other  points. 


rad.  -  offset 
These  formulas  are  derived  from  the  similar  triangles,  c  A  o, 

E  B  O,   C  H  B,  B  H  O,  B  C  O,  B  K  E,  and  B  K  GK 
EIGHTH  METHOD. 

By  Ordinates  to  Chords. 


1.  To  find  the  middle  ordinate  (m). 

A.  Given,  the  tangents  on  the  ground. 


414  APPENDIX  0. 

A E  bisects  c A D.   Hence,  DE  :  EC  : :  AD  :  ACL 
And  DE  :  DE  +  EC  :  :  AD  :  AD  +  AC; 

or,  DE:DC::AD:AD  +  AO. 

Hence,  DE  =  ^-^  =  m. 

AD  +   A  C 

Also,  DE:EC::AD:AC::  cos.  C  A  B  :  1. 

D  E  :  D  E  +  E  c  :  :  cos.  CAB:  cos.  c  A  B  +  1. 

Hence,  m  =  DE  =  1  C08'  C  AB    . 

1  +  COS.  CAB 

B.  Given,  the  radius  and  chord. 

OAS  =  AD'  +  DO'  =  (lc)4+  (OE  —  DE)',  or,  r*  =  ic'+(r-  mf 

2  r  m  =  i  c'  +  m*. 

Hence,  m  =  r  -  ^/(IA  —  \  c8). 

Approximately.    In  the  equation 

2  r  m  =  \  c*  +  m', 

neglecting  the  last  term  in  the  second  member  (which  is  yeiy 
small  in  railroad  curves),  we  have, 

c" 
m-S~r 

C.  Given,  radius  and  chord  of  half  the  arc  =  c7. 
From  the  similar  triangles,  BAD  and  A  o  M,  we  have, 

AO  :  AM(=iAE)  ::  AE  :  ED. 
Hence, 

A  E*  c'» 

E  D  = ,  or.  m  =  s — • 

SAO  2  r 

D.  Given,  radius  and  tangent. 

DE  =  DC  —  CE  =  DO  —  (OC  —  OE) 
=  DC—  [V(AO*  +  ACS)-AO]  =DC  + AO- 

Hence,        DE  =  WI  =  DC  +AO  —  /^/(A  o'  +  A  <?). 

E.  Given,  the  "  tangential  angle." 

E  D  =  A  D  .  tan.  E  A  D. 

Hence,  E  D  =  m,  =  $  c  .  tan.  i  6°. 


APPENDIX  C. 


415 


2.  To  find  intei-mediate  ordinates.    (Fig.  13.) 

Let  D  o,  the  distance  of  the  foot  of  the  required  ordinate  from 
the  middle  chord  be  represented 
by/ 

The  required  intermediate  ordi- 
nate, A, 

FQ  =  FH—  OH, 

we   will   find   F  H   and   o  H   in 
turn. 

F  H*  =  H  L  x  HI  =  (OL  + 

Hence,  F  H  =  //(r1  -  /• ). 

G  H"  =  AK3  =IK  x  KL=(OI  —  OK)(OL 


Hence,  o  n  =  ^/(r1  —  $  c1  ). 

Then,  F  o  =  ^/(ra  -/')  -  ^/(r* 

Approximately.    (Fig.  14.) 


GM  — DP  =  EN— (ED  +  PN). 


416  APPENDIX  C. 

Omit  the  subtrahend,  as  very  small  compared  with  E  x,  and  we 
have, 


COMPOUND  CURVES. 

A  single  arc  of  a  circle  uniting  two  tangents,  must  meet  them  at 
equal  distances  from  their  point  of  intersection  or  vertex.  If  it  be 
required  to  unite  two  tangents  by  a  curve  meeting  them  at  unequal 
distances  from  the  vertex,  a  compound  curve  must  be  employed, 
composed  of  two  or  more  arcs  of  circles  of  different  radii.  • 

A  fundamental  condition  is  that,  the  centres  of  the  two  adjoining 
arcs  and  their  point  of  meeting,  must  lie  in  the  same  straight 
line ;  since  these  arcs  must  have  a  common  tangent  at  their  point 
of  meeting. 

An  infinite  number  of  pairs  of  curves  would  satisfy  the  preced- 
ing conditions,  consequently,  another  condition  must  be  intro- 
duced. This  may  be  that  one  radius  shall  be  given,  or  that  the 
difference  of  the  two  radii  shall  be  a  minimum ;  or  their  ratio  a 
minimum,  etc. 

PROBLEM  I. 

It  is  required  that  the  ratio  of  the  two  radii  shall  be  a  minimum. 

In  this  case  the  common  tangent  will  be  parallel  to  the  line  A  z. 

Analytically.    Let  I  and  t'   be  the  Fig.  15. 

two  tangents,  i  A  and  I  z ;  r  and  r'  the 
corresponding  radii ;  <p'  and  <p  the 
angles  comprised  by  the  curves,  or  their 
angulr.r  lengths ;  and  a  the  angle  A I  z. 
Put 

m  —  ^{t*  +  f*  —  2t .  t' .  cos.  a.) 

Then, 

7'  =  2 1' .  sin. a  '  (m  +      ~ '  )• 

~~  2 1 .  sin.  a  ' 

O' 

I' .  sin.  a.                     .        ,       t .  sin.  a 
sin.  q>  =  .  sin.  q>  = . 


APPENDIX  C. 


417 


PKOBLEM  II. 

It  M  required  to  make  the  difference  of  the  two  radii  a  minimum, 
t-  t' 


r  =  t .  tan.  i  a  + 


2  cos.  i  a 


f  .  tan.  i  a  — 


t-f 
2  cos.  i  a' 


=  <p=9    —  i  a. 


PROBLEM  III. 

When  one  radius  is  giren  to  find  the  other. 

By  construction.  Draw  perpendiculars  at  A  and  z.  Set  off  the 
given  radius  on  each  of  them,  from  A  to  some  point,  o,  and  from  z 
to  some  point,  p.  Join  o  p,  and  bisect  it  by  a  perpendicular.  This 
perpendicular  meets  the  perpendicular  from  z  in  o'.  o  and  o'  are 
the  desired  centres,  and  the  two  curves  will  unite  on  the  line 
through  these  points. 

Analytically*  Let  A  z,  the  angles  IAZ  and  IZA,  and  the  radius 
A  o  =  r,  be  given,  to  find  the  second  radius  r1. 

From  A  run  a  curve  with  the  first  Fig.  10. 

radius  to  D,  where  the  tangent,  D  E,  Ix 

becomes  parallel  to  z  i.  The  line, 
z  D,  prolonged  will  meet  the  curve  at 
the  common  tangent  point,  c. 

'  —  ZD 

+  2  sin.  c  z  i 

When  the  angle  at  z  is  greater  than 
the  angle  at  A,  the  formula  becomes, 

ZD 


2  siii.  c  z  i* 


In  the  field  the  point,  D,  may  be  found  by  laying  off  the 
angle,  IAD  =  £(IAZ  +  IZA),  and  measuring  the  distance,  A  D 
=  2r  .  sin.  |(IAZ  +  IZA). 

REVERSED   CURVES. 

If  the  two  branches  of  the  curve,  instead  of  both  lying  on  the  same 

*  From  Henck's  Field  Book. 
18* 


418 


APPENDIX  C. 


side  of  the  common  tangent,  as  in  "  Compound  Curves,"  are  on 
opposite  sides,  it  is  called  a  "  Reversed  Curve." 
Fig.  17. 


PROBLEM 


When  the  tangents  are  parallel,  and  both  curves  are  to  have  the  same 
radiiis,  to  find  the  radius,  r. 

When  the  tangents  are  parallel,  the  point  of  reversed  curvature 
is  on  the  line  joining  the  tangent  points ;  and  if  the  two  radii  are 
equal,  it  is  the  centre  of  the  line. 

Let  the  distance  A  B,  Fig.  17,  be  represented  by  a,  and  the  per- 
pendicular distance  between  the  tangents,  by  d.  Then  we  have, 

'-'* 

PROBLEM  IL 

When  the  tangents  are  parallel,  and  one  radius,  r,  is  given,  to  find 
the  other  radius,  r'. 

a* 


2rd 
a  ' 


I,  BC=AB  —  AC. 


PROBLEM  III.  . 

When  the  tangents  are  not  parallel,  and  both  curves  are  to  have  tfa 
tame  radius,  r,  the  tangent  points  being  given.    (Fig.  18.) 
sin.  B  P  c 

r  =5  B  Y  -: : :. 

sin.  o  +  sin.  c 


APPENDIX  C. 

Sin.  B  p  c  =  i  (cos.  A  B  T  +  cos.  B  Y  z) ; 
o  =  270"  —  BPC  —  ABY; 
cf  =  270°  —  BPO  —  BTZ. 

Fig.  18. 


419' 


PKOBLEM  IV. 

When  the  tangents  are  not  parallel,  and  one  of  the  tangents,  r,  it 
given,  to  find  the  other  tangent,  r1. 

Run  with  the  given  radius  to  some  point,  D,  where  the  tangent, 
D  E,  is  parallel  to  A  B,  and  then  apply  Prob.  I.  To  find  D,  lay  off 
ZYD  =  iEFB,  and  make  Y  D  =  2  r  sin.  £  B. 

To  lay  out  a  compound,  or  reversed  curve,  run  to  the  point  of 
common  tangency  of  the  two  branches  of  the  curve,  by  one  of  the 
methods  given.  At  that  point  get  on  the  tangent,  and  then  run 
out  the  remaining  branch  in  the  usual  manner. 


€30  APPENDIX  D. 


APPENDIX  D. 


:  ESTIMATIOH. 

General  Principles. 

WE  have  to  determine :  1st,  The  cost  of  the  raw  material ;  2d, 
Time  employed  in  working  on  it ;  3d,  Price  of  a  unit  of  this  time. 

1.    First  Cost. 

This  varies  with  the  locality,  demand,  etc.    The  waste  in  shap- 
ing a  material  must  be  allowed  for.    In  common  cut  stone  it  is 
about  -|\j ;  in  converting  round  timber  to  hewn,  about  £. 
2.    Time. 

The  time  in  which  an  average  workman  will  perform  a  certain 
amount  of  work  of  any  kind,  is  called  the  "  Constant"  of  labor  for 
that  work,  it  being  nearly  the  same  for  all  times  and  places.  To 
get  the  cost  of  that  work  it  is  only  necessary  to  multiply  this  con- 
stant by  the  price  of  labor  for  that  unit  of  time. 

APPLICATION  TO  ROAD-MAKING. 

A .  Constants  for  Excavation. 

The  table  on  page  126  gives  for  one  cubic  yard  of  excavation, 
previously  loosened,  including  throwing,  for  common  earth,  1.25 
hours  to  £3  of  an  hour;  loose  and  light  earth,  1.25  hours;  mud, 
1.43  hours  to  .62  hour ;  clay  and  stony  earth,  2.5  hours ;  rock,  after 
blasting,  4.5  hours.  Other  experiments  for  "hard  pan,"  4.2  hours; 
compact  sand,  .43  hour. 

The  table  on  page  128  gives  for  excavating  earth,  and  loading  it 
into  barrows,  a  constant  of  .42  hour,  and  for  excavating  and  load- 
ing it  into  horse-carts,  .8  hour. 

Cole's  Erie  Canal  Experiments  give  .47  hour  for  burrows.  A 
man  has  shovelled  into  a  -wagon  at  the  rate  of  .48  hour.  The 
constants  from  the  bottom  of  page  125  are  for  shovelling  into  a 


APPENDIX   D. 


421 


cart,  earth  previously  loosened.     Gravel  and  clay,  1  hour ;  loam, 
.83  hour ;  sandy  earth,  .71  hour ;  average  for  all,  .6  hour. 

Excavating  clay  tow-path  and  depositing  it  behind  the  bank,  1.8 
hours. 

B.  Barrow  Work. 

Constant  for  wheeling  1  cubic  yard  100  feet : 

1.  Page  126  gives,  for  common  earth,  from  .5  to  .3,— average,  A 
hour. 

2.  Page  128  gives,  average  .44  hour. 

3.  Birmingham  Railroad,  page  128,  gives  .34  hour. 

4.  Morin  says  one  man  can  wheel  400  Ibs.  (=3  cubic  feet), 
20,000'  in  10  hours.    Constant  per  .45  hour.    (No  return.) 

5.  Gauthey  says  removing  1  cubic  metre  a  distance  of  30  metres, 
takes  .5  hour:  constant  per  yard  for  100'  =  .38  hour. 

6.  Erie  Canal  work  with  barrows  holding  -rV  cubic  yard ;  wheel- 
ers travel  250'  per  minute,  on  a  level  run ;    delays  starting,  etc.,  J 
minute.     Constant  per  yard  for  100'  =  .275  hour. 

Work  of  loading  into  a  barrow  and  wheeling  common  earth,  the 
following  length  of  run-way,  for  a  day  of  10  hours,  on  the  Erie 
Canal  enlargement: 


Length,  in  feet, 
of  rnn-way. 

Cubic 
yards. 

Constant,  in 
hours,  per  yard. 

Cost  per  yard, 
at  $1  per  day. 

50 

100 
150 
200 
300 
'    400 
500 

16 
14 
12 
10 
8 
7 
6 

0.625 
.71 
.833 
1.00 
1.25 
1.428 
1.67 

6.25 
7.1 
8.33 
10.00 
12.5 
14.28 
16.7 

The  above  table  gives  a  constant  of  .24  hour  for  each  hundred 
feet  after  starting. 

C.   Wagon  Work. 

Average  performance,  on  10  miles  of  the  Erie  Canal,  of  the  men 
in  loading  wagons,  including  picking,  and  loss  of  time  in  waiting 
for  wagons  to  come  in,  etc.,  was,  per  day  of  12  hours :  sand  and 
loam,  15  cubic  yards,  constant,  .8  hour ;  clay  and  gravel,  12  cubic 
yards,  constant,  1  hour ;  hard  pan,  4  yards,  constant  3  hours ;  stiff 
clay  (earth  of  H  men.),  10  yards,  constant,  1.2  hours. 


422 


APPENDIX  D. 


Six  men  can  work  to  best  advantage  in  loading  wagons.  They 
can  fill  a  wagon  containing  $  cubic  yard  in  2  minutes.  Unload- 
ing and  other  delays  take  3  minutes,  and  100  feet  at  each  end  for  a 
turning  space  should  be  added  to  the  hauling  distance.  The  horses 
travel  at  about  the  rate  of  2±  miles  per  hour,  or  220'  per  minute. 

"Work  done  in  a  day  of  10  hours,  by  a  pair  of  horses,  working  on 
a  level  road,  with  a  common  wagon : 


Distance  in  feet. . . . 
Cubic  yards  per  day 
Constant  per  yard. . 


100 

61 

0.16  h. 


200 

53 

0.19  h. 


500 

40 

0.25  h. 


1000|1500  2000 
21     17 


Up  a  slope  of  100'  per  mile  (=  -h)  only  J  as  much  can  be  drawn. 
Up  a  slope  of  260'  per  mile  (1  in  20),  only  $  as  much  can  be  drawn. 


D.  Railway  Work. 

Work  done  on  a  rail  track  with  horses  kept  constantly  moving, 
and  hauling  on  a  level  three  loaded  cars,  containing  1|  yards  each, 
at  2i  miles  per  hour. 


Distance  in  feet  
Cubic  yards,  per  day. 

1000 
225 

2000 
127 

3000 
90 

4000 
69 

5000 
56 

10000 
29 

2000o! 
15 

LIMITING  DISTANCES. 

A  limiting  distance  for  any  mode  of  transportation  is  that  at 
which  that  mode  becomes  more  expensive  than  some  other  mode. 

The  first  means  of  moving  earth  very  short  distances  is  by  throw- 
ing it  with  the  shovel,  which  can  be  done  12'  horizontally  and  5' 
vertically.  For  twice  that  distance  two  men  may  throw  twice, 
and  so  on.  The  scraper  is  cheaper  for  more  than  12'. 

For  long  distances  and  heavy  work,  rails  should  always  be  laid 
on  which  one  horse  can  draw  several  cars,  which  can  be  dumped 
where  desired. 

There  is  a  certain  distance  at  which  the  various  modes  of  trans- 
port become  successively  more  expensive  than  some  other.    Tlr 
limit  is  best  found  by  putting  tabular  results  of  experiments  i 
diagram. 


APPENDIX  D.  423 

The  average  of  many  experiments  give  the  following  limiting 

distances.     Men  shovelling  to  24'  in  two  throws. 
Scraper,    ...        .      thence  to  100' 

Barrow "       "    200 

One-horse  cart,          .    .       "       "      $  mile 
Two-horse  wagons,    .    .       "       "     J      " 
Railroad  with  horses  thence  to  1-J  miles. 
Railroad  with  locomotive  for  greater  distances. 
The  horse  railroad  should  be  used  for  less  distances,  if  the  amount 

to  be  moved  is  large,  which  will  also  effect  the  preceding  limits. 


424  APPENDIX  E. 


APPENDIX  E. 


TtJKNELB. 

WHEN  the  depth  of  an  excavation  passes  beyond  a  certain 
limit,  it  becomes  cheaper  to  tunnel.  To  determine  when  to  change 
from  open  cutting  to  tunnel  :  let  e  equal  the  cost  of  excavation  per 
cubic  yard,  t  equal  the  cost  of  the  tunnel  per  running  foot,  b  equal 
the  base  of  the  excavation,  s  equal  the  ratio  of  the  side  slopes,  and 
x  the  unknown  depth  at  which  the  costs  of  excavating  and  tunnel- 
ling are  equal.  Then  we  have  : 

Cross-section  of  excavation  =  x  (b  +  s  x), 

Contents  for  one  running  foot          =  x  (b  +  sx\ 

Cost  of  running  foot  of  excavation  =         *          x  e. 

"  tunnel  =  t, 

Hence,  «£-•*  x.-4 


A  somewhat  greater  depth  than  that  deduced  from  the  formula 
would  be  arrived  at  before  beginning  to  tunnel,  because  of  the  un- 
certainty and  delays  of  tunnel  work. 

Dimensions.  —  "Width  from  24  to  30  feet  (for  double  track),  height 
from  18  to  25  feet. 

The  Mount  Cenis  tunnel  is  26i  ft.  wide,  20  ft.  8  in.  above  the 
rails,  and  7  miles  1044  yds.  long.  There  is  no  shaft.  The  depth 
of  tunnel  below  the  summit  of  the  mountain  is  one  mile. 

The  dimensions  adopted  for  the  numerous  tunnels  on  the  Central 
Pacific  Railroad  was  :  width  16  ft.,  height  19,  consisting  of  a  rect- 
angle at  the  bottom  16  x  11,  and  a  semicircle  at  the  top,  16  ft.  in 
diameter. 


APPENDIX  E.  425 

The  Hoosic  tunnel  is  to  be  24500  ft.  long. 

Laying  them  out. — The  centre  line  is  first  set  out  on  the  surface 
of  the  ground  with  great  accuracy.  Then  the  line  is  carried  into 
the  adits  and  down  the  shafts. 

Construction. — The  work  is  commenced  with  a  "  heading"  or 
"  driftway"  about  6  ft.  square,  sometimes  at  the  bottom,  and  some- 
times at  the  top.  In  solid  rock  it  is  better  to  carry  in  the  heading 
at  the  top.  This  driftway  is  afterward  enlarged  to  the  full  cross- 
section.  Tunnels  in  earth  or  loose  rock  are  lined  with  timber  or 
masonry. 

When  the  tunnels  are  long,  shafts  are  sunk  at  convenient  places 
in  order  to  expedite  the  work.  From  the  bottom  of  the  shaft  the 
excavating  is  carried  on  both  ways,  the  earth  being  raised  in 
buckets. 

The  usual  dimensions  for  shafts  are  from  9  to  12  ft.  in  diameter. 
If  rectangular,  about  8  x  12  ft  It  is  recommended  by  some  to 
carry  the  shaft  down  at  the  side  of  the  tunnel,  instead  of  over  the 
centre.  Sometimes  they  are  impracticable,  as  at  Mount  Cenis. 

When  the  material  to  be  excavated  is  rock,  blasting  becomes 
necessary.  See  page  160. 

Nitro-glyceriue  is  extensively  used  for  rock  blasting.  Much 
more  rapid  progress  can  be  made  with  it  than  with  powder.  The 
drills  used  are  smaller,  fewer  boles  are  required,  and  the  rock  is 
broken  into  smaller  pieces.  It  is  much  less  expensive,  and  if 
manufactured  on  the  ground  where  it  is  used,  and  handled  with 
proper  care,  it  seems  no  more  dangerous  than  powder. 

At  Mount  Cenis  the  drilling  was  done  by  machinery,  worked  by 
air,  which  was  compressed  by  water  power  near  the  tunnel.  The 
compressed  air,  after  doing  its  work,  was  discharged  from  the 
machine  and  served  for  ventilation. 

The  alignment  inside  the  tunnel  is  secured  by  wooden  plugs, 
inserted  into  drill  holes  in  the  roof.  The  exact  centre  line  is 
marked  by  tacks,  driven  into  the  plugs,  to  which  a  piece  of  cord 
is  fastened. 

Progress.— This  depends  on  the  rapidity  with  which  the  "  head- 
ing" or  "  driftway"  can  be  pushed  forward,  as  the  "  bottom"  can 
be  taken  out  much  more  rapidly.  It  varies  from  2  ft.  per  day  in 
hard  granite,  to  10  or  12  ft.  in  soft  rock  and  earth.  The  slowness 


426  APPENDIX    B. 

of  the  work  is  due  to  the  lack  of  room,  and  the  disadvantage  of 
working  against  the  face  of  the  rock. 

Cost.—  In  the  United  States  tunnels  cost  from  $2.00  per  cub.  yd. 
in  soft  slate  to  $7.00  in  hard  graywacke. 

On  the  Baltimore  and  Ohio  Railroad  the  average  cost  per  cub. 
yd.,  without  counting  the  shafts,  was  $2.60,  the  length  being  from 
100  to  1200  ft.  With  the  same  material,  excavations  hi  the  open 
cutting  cost  about  one-fourth  as  much. 

The  Bergen  tunnel  for  the  Erie  Railroad  is  4300  ft.  long,  23  ft. 
high,  and  28  ft.  wide.  It  cost  about  $1,000,000. 

The  Summit  tunnel  on  the  Central  Pacific  Railroad  was  1659  ft 
long  with  one  shaft,  and  cost  about  $15.00  (gold)  per  cub.  yd.  with 
powder,  and  $10.00  with  nitro-glycerine. 

In  England  tunnels  for  single  track  usually  cost  from  $35.00  to 
$75.00  per  running  foot.  Some  have  cost  as  high  as  $150.00  per 
running  foot. 

In  earth  the  mere  excavation  is  a  small  part  of  the  expense.  In 
one  English  tunnel  the  cost  of  excavating  was  only  about  one 
fourth  as  much  as  the  propping  and  arching. 

The  principal  difficulties  met  with  in  tunnelling  are  want  of 
ventilation  and  drainage.  Headings  can  be  driven  but  a  few  hun- 
dred feet  before  artificial  ventilation  becomes  necessary.  The  air 
being  confined  is  soon  rendered  impure  by  the  respiration  of  the 
men  and  the  smoke  of  the  lamps ;  and  after  each  blast  the  smoke 
of  the  powder  would  make  it  impossible  to  continue  the  work  for 
some  time.  By  forcing  air  through  pipes  into  the  heading,  the 
smoke  is  at  once  driven  out  and  pure  air  supplied  to  the  men. 

When  a  tunnel  enters  a  hill  on  an  "  up  grade"  there  is  no  diffi- 
culty about  drainage  -  but  when  the  work  is  on  a  "  down  grade," 
or  from  the  bottom  of  a  shaft,  the  water  which  collects  in  the 
working  must  be  lifted  in  buckets,  or  pumped  out 


APPENDIX  F.  427 


APPENDIX  F. 


General  Principles.— A.  body  is  to  be  supported  over  an  inacces- 
sible space.    Its  weight  is  a  force  acting  vertically.    It  can  be 
Fig.  1.  supported  only  by  the  ac-  Fig  2> 

tion  of  two  oblique  forces, 
or  pieces  supporting  it  by 
their  resistance  to  compres- 
sion or  extension ;  i.  e.,  by 
acting  as  struts  or  lies.    For 
example,  Figs.  1  and  2. 
Every  method  of  sustaining  a  material  point  in  space  may  be 
reduced  to  these  two.    A  beam  combines  an  infinite  number  of 
pairs  of  struts  and  pairs  of  ties. 

A  series  of  points  are  usually  supported,  as  in  Figs.  1  and  2,  at 
such  distances  apart  that  a  beam  resting  on  two  of  them  will 
support  the  load  between  them.  The  combinations  supporting 
the  several  points  form  a  truss,  the  beam  being  nature's  truss. 

Weights  to  be  supported.— The  greatest  possible  load  is  a  crowd 
of  men.  Equal  70  pounds  per  square  foot.  A  drove  of  cattle  is 
40  pounds  per  square  foot.  A  double  row  of  the  heaviest  loaded 
wagons,  with  horses,  gives  600  pounds  per  running  foot.  Calling 
each  row  six  feet  wide,  we  have  50  pounds  per  square  foot,  A 
heavy  freight  train  weighs  half  a  ton  per  running  foot.  A  row  of 
engines  weighs  one  ton  per  running  foot.  If  the  track  be  double, 
of  course  the  weight  and  the  strain  will  be  double. 

The  weight  of  the  bridge  itself,  is  the  first  thing  to  be  determined 
in  proportioning  a  bridge.  The  weight  of  a  good,  single-track 
wooden  bridge,  per  running  foot  of  span  =0.3  ton  gross  (invari- 
able), -f  0.15  ton  for  a  span  of  150  ft.  (the  latter  item  increasing  as 


428  APPENDIX  F. 

the  square  of  the  span),  +  0.3  ton  for  the  increase  of  the  weight  by 
velocity.  This  is  Trautwine's  rule.  Thus  for  a  span  of  150  feet, 
we  will  have  :  weight  of  bridge  =  150  x  (0.3  +  0.15  +  0.3)  = 
150  x  0.75  =  112|  gross  tons  =  1630  pounds  per  running  foot. 

For  two  hundred  feet  span,  the  second  item  is  obtained  thus: 
ISO2  :  2002  :  :  0.15  T  :  0.222  T.  Hence,  weight  per  running  foot 
is  0.3  +  0.222  +  0.3  =  0.822  T  =  1850  pounds. 

An  Erie  Canal  farm  bridge  of  six  open  panels  of  72  feet  span, 
contains  10  cubic  feet  of  timber  per  running  foot.  One  of  43  feet 
span  contained  the  same. 

A  double  road  bridge  over  the  canal  of  90  feet  span  contains 
22  cubic  feet  of  timber  per  running  foot.  A  railroad  bridge  of  four 
panels  of  30  feet  span  contains  20  cubic  feet  per  running  foot.  One 
of  Long's  bridges,  100  feet  long,  contains  42,000  feet  B.  M.,  or  35 
cubic  feet  per  running  foot.  A  McCallum's  bridge  of  200  feet  span 
contains  50  cubic  feet  of  timber  per  running  foot,  or  averages  1500 
to  2000  pounds  per  running  foot. 

Iron  truss  bridges  weigh  from  1000  to  2000  pounds  per  running 
foot.  Wood  weighs  from  30  to  60  pounds  per  cubic  foot— average 
40  pounds.  Cast  iron  weighs  450  pounds,  and  wrought  iron  480 
pounds  per  cubic  foot. 

In  calculating  bridges,  assume  some  approximate  weight  for  the 
bridge,  and  after  determining  the  necessary  sizes  (and  consequently 
weights)  of  the  different  parts,  the  calculations  should  be  again 
made,  using  the  weight  of  the  bridge  just  found. 

Classification.— Bridges  will  be  here  classified  ;  First,  As  to  their 
material :  As  wood,  stone,  iron,  or  brick,  and  these  subdivided ; 
Secondly,  As  to  the  manner  in  which  their  points  are  supported, 
viz.,  Trabeate,  Arcuate,  or  Suspension. 

WOODEN  BRIDGES. 

Trabeate. 

The  simplest  form  of  a  bridge  is  a  plank.  Next  to  it  is  a  pair  of 
timbers  with  planks  crosswise  upon  them.  For  a  hasty  bridge, 
two  trunks  of  trees  with  smaller  trunks  laid  across  them. 

In  calculating  bridges  of  this  kind,  the  timbers  are  considered  to 
be  supported  at  both  ends  and  loaded  uniformly  with  the  greatest 


APPENDIX  F. 


429 


load  that  can  come  upon  them.  To  determine  the  weight  any 
given  beam  hi  this  condition  will  bear,  or  the  size  necessary  to 
bear  a  given  weight,  we  have  the  formula, 


In  which  w  represents  the  breaking  weight,  6  and  Ji  the  breadth 
and  height  in  inches,  L  the  length  hi  feet,  and  s  a  coefficient  found 
by  experiment.  For  common  American  timber  s  varies  from  300 
to  700  ;  for  white  pine  it  is  410  ;  for  white  oak,  580  ;  for  tama- 
rack, 300  ;  for  hemlock,  380  ;  for  red  pine,  510  ;  for  white  ash,  600  ; 
for  hickory,  700.  The  safe  load  may  be  taken  at  £  the  breaking 
weight. 

When  a  span  becomes  too  long  for  a  single  beam,  "  corbels"  are 
used,  as  in  Fig.  3.  The  strain  on  them  is  Fig.  3. 

like  that  of  a  beam  fixed  at  one  end  and 
loaded  uniformly.  They  may  be  strengthened 
by  struts. 

A  series  of  such  bridges  resting  on  simple 
piles,  is  known  as  "  pile  bridging"    It  is  the 
usual  way  in  which  railroads  cross  shallow  waters.    "When  high 
above  the  water  they  are  called  "  trestle  work"  bridges. 

Fig.  4  shows  the  arrangement  of  the  piers  for  the  railroad  pile 
bridge  across  the  South  Platte.  The 
piers  are  placed  sixteen  feet  apart. 
There  are  four  piles  about  one  foot 
in  diameter  in  each  pier;  the 
middle  ones  being  5  feet  apart,  and 
the  outside  ones  4$  feet.  Sway 
braces,  3"  x  10"  and  14  feet  long, 
are  bolted  to  the  piles. 

The  greatest  trestle  bridge  is  the 
Portage  High  Bridge.  It  is  800  feet 
long  and  1$0  feet  high.    Contains  1,600,000  feet  B.  M.  of  wood, 
and  109,000  pounds  of  bolts. 

Comparative  cost  of  trestle  work  and  earth  work.  For  five  feet 
high,  trestle  work  costs  four  times  as  much  as  earth  work.  The 
Portage  Bridge  cost  only  a  quarter  that  of  earth  work.  The  cost 
of  earth  work  increases  nearly  as  the  square  of  the  heights.  The 


430  •  APPENDIX  P. 

cost  of  trestle  work  increases  about  as  the  j-  power.  Making  the 
heights  the  abscissas,  and  the  cof.t  the  ordinates,  the  curve  for  the 
earth  work  will  be  a  common  parabola,  and  for  trestle  work  a 
semicubical  parabola. 

CLASSIFICATION  OP  BRIDGE  FBAMES. 

CLASS  I.  The  oblique  pieces  all  resist  compression. 

1.  The  weight  is  transferred  to  the  abutments  directly. 

2.  The  weight  is  transferred  to  the  abutments  indirectly;  as 
Long's,  Howe's,  etc. 

3.  Combinations  of  sub-classes  1  and  2 ;  as  Latrobe's. 

CLASS  II.  The  oblique  pieces  all  resist  extension. 

1.  The  weight  is  transferred  to  the  abutments  directly;  as  Boll- 
man's,  etc. 

2.  The  weight  is  transferred  to  the  abutments  indirectly,  being 
conveyed  to  the  oblique  ties  by  vertical  posts  ;  as  Linville's,  etc. 

3.  Combinations  of  sub-classes  1  and  2 ;  as  Fink's. 

CLASS  III.  The  oblique  pieces  are  alternately  compressed  and  extended. 

The  weight  is  transferred  to  the  abutments  indirectly ;  as  War- 
ren's, etc. 

Arched  Bridges  are  polygonal  modifications  of  Class  I. 
Suspension,  Bridges  are  polygonal  modifications  of  Class  II. 

CLASS  I.  The  oblique  pieces  all  resisting  compression. 

1.  When  the  weight  is  transferred  to  the  abutments  directly,  as 
in  Figs.  5,  6,  7,  etc.  Fig  5 

In  Fig.  5,  the  middle  point  being  sup- 
ported, twice  the  span  can  be  obtained  with 
the  same  strength  of  beam.  One-half  the 
weight  is  borne  by  the  struts.  In  calculating  — j—^ 


'he  strain  on  a  pair  of  struts,  as  A  B  and  A'  B>  — 

the  effect  is  the  same,  whether  the  weight  — 

rests  directly  on  the  top  of  the  struts  or  is  suspended  beneath 

them. 


APPENDIX  P. 


431 


CALCULATIONS. 

Construct  a  parallelogram,  having  for  one  diagonal  a  line  B  F, 
representing  the  number  of  units  in  the  weight,  Fig.  6. 

and  having  its  sides  parallel  to  the  struts. 
These  sides  will  represent  the  strains  on  the 
beams  to  which  they  are  parallel.  Let  t 
represent  the  thrust  in  the  direction  of  their 
length,  h  the  horizontal  thrust,  and  w  the 
weight  Then  we  have, 

W  :  I  :  :  BP  :  BD; 

:  :  2  B  E  :  B  D  , 

:  :  2  B  C  :  B  A. 


He^ce, 

By  similar  triangles, 


w  —  =  *w  ^  =4  w  cosec.  A. 
B  c  rise 


Hence, 


B  C   :  A  C. 

w  span 


:  7i  : :  rise  :  \  span. 


Any  change  in  the  obliquity  of  the  beams  increases  or  dimin- 
ishes the  strains,  as  can  readily  be  seen  from  the  formulas.  The 
length  of  the  beams  has  no  effect  on  the  stresses,  but  the  strength 
of  a  beam  decreases  as  its  length  increases. 

NOTE.— Safe  loads  for  wooden  posts,  whose  crushing  load  is 
6000  Ibs.  per  square  inch.  • 


Ratio  of  length  to  side. 

1 

10 

15..., 

20 

25 

80 

35 

40 

45 

50 

55 

60 

65 

70 


Safe  stress  in  lb?.  per  sq.  inch. 
.    900 


420 

340 

280 

225 

175 

130 

105 

85 

70 

CO 


432 


APPENDIX   F. 


If  the  post  is  not  square,  take  the  ratio  of  the  length  to  the 
smallest  dimension. 

Two  points  may  be  supported  in  space,  as  in  Fig.  7.    Each  pair 
has  one  long  and  one  short  strut ;  we  will  Fig.  7. 

calculate  one  pair  separately.    Let  the  pair  at  _[ 
the  left  be  represented  by  Fig.  8.  ^ 

Let  the  wt.  =  1500  Ibs.    Let  each  inch  of  ti- 
the diagonal  represent  500  Ibs.    Let  the  angle  X 
of  the  beams  =  100",  the  one  making   an  -~ 
angle  of  60°  with  the  vertical,  and  the  other  " 
an  angle  of  40°.    Required  the  strain  on  the 
two  beams,  A  B  and  A  c.    (The  Fig.  is  not  drawn 
to  scale.) 

1.  Graphically.    Set  off  on  the  vertical  3", 
and  complete-the  parallelogram  as  before.   The 
proportions  of  the  wt.  borne  by  B  and  c  are, 
respectively,  A  a  =  D  n  and  A  H  =  D  o.     When 

B  and  c'are  at  different  heights,  to  find  the  portion  of  the  wt.  borne 
by  each,  draw  the  lines,  not  horizontal,  but  parallel  to  B  c. 

2.  Trigonometrically. 

w  :  strain  onAB::AD:AE::  sin.  A  E  D  :  sin.  A  D  E. 
sin.  A  D  E 


strain  on  A  B  =  w 


AD 


sin.  A  E  D 
A  F  : :  sin.  A  F  D 


sin.  A  D  F. 


sin.  A  D  F 

strain  on  A  c  =  w  — 

sin.  A  F  D 


Hence, 

Again,    w  :  strain  on  AC 

Hence, 

Substituting  these  values  in  the  formula,  .we  have, 

strain  on  A  B  =  1500  x  — 

-     sin.  80 

strain  on  A  c  =  1500  x  S4n^->—  =  979. 
sin.  80 

Resolving  these  strains  into  then-  vertical  and  horizontal  com- 
ponents, we  shall  find  that  the  horizontal  pressure  of  one  of  the 
beams  exactly  equals  that  of  the  other,  whatever  be  the  difference 
of  their  inclination  to  the  vertical,  and  that  the  sum  of  the  two 
vertical  components  equals  the  whole  weight  The  numerical 
calculation  of  these  components  is  made  as  before  trigonomel- 
rically.  ^JV 

When  the  span  and  heights  of  the  struts,  and  hence  their  lengths 


APPENDIX   F. 


433 


are  given,  we  have  more  simply:  the  weight  supported  at  either 


end  =  w  x 


non-adjacent  segment 


whole  span 
That  id   the     Weight  supported  at  B 

Weight  supported  at  c 


KC 
BC' 


Thrust  on  A  B  =  weight  on  B  x  —  ; 
"       "  A  c  =  weight  on  c  x  — . 

AK 


K  C 


Horizontal  thrust  =  weight  on  B  x  — _  =  weight  on  C  x  — . 

Instead  of  supporting  the  two  points  by  two  pairs  of  struts,  as 
Fis.  9.  in  Fig.  7,  we  may  ern-  pig.  j0. 

ploy  two  struts,  and  a 
straining  beam,  Fig.  9. 
The  calculations  are  the 
same,  as  for  Fig.  13. 

Four  points  may  be 
supported  iu  a  similar 
manner  by  two  pairs  of  struts  and  two  straining  beams,  as  in 
Fig.  10. 

This  principle  may  be  extended  to  great  spans,  but  long  timbers 
are  hard  to  get  and  are  weaker.  A  bridge  at  Wettingen,  on  thia 
plan,  has  a  span  of  397  feet. 

In  many  cases,  supports  from  below  may  be  objectionable,  as 
exerting  too  much  thrust  against  the  abutments,  and  being  liable 
to  be  carried  away  by  freshets,  etc.  The  beams  must  in  such  cases 
b2  strengthened  by  supports  from  above,  as  in  the  following  class. 
2.  When  the  weight  is  transferred  to  the  abutments  indirectly, 
being  conveyed  to  the  oblique  struts  by  vertical  ties. 

The  simplest  form  of  this  class  is  a  pair  of 
struts,  Fig.  11.  The  calculations  for  this  are 
the  same  as  for  Fig.  5. 

Bridges  built  on  this  plan  can  be  used  on 
railroads  for  spans  of  from  10   to  25  feet. 
For  longer    spans  (say  up  to  85   feet)  two 
struts  and  a  straining  beam  may  be  used,  Fig.  12. 
19 


Fig.  11. 


434 


APPENDIX  F. 


Calculations.  With  loads  w  and  w'  on  c  and  c',  the  stresses  are 
analogous  to  Fig.  6.  Consider  the  upward  reaction  at  A  and  A', 
which  are  each  equal  to  FiR.  12. 

w.     Then,    the    triangle, 
ABC,  gives  stress  on  AC 

=  w  - — ;  horizontal  stress 

B  C 

=  w  —5,    All  the  stresses 

B  c  • • 

are  the  same  as  if  the  struts,  A  c  and  A*  c',  were  produced  upward 
to  meet,  and.  the  whole  load  (w  +  w')  placed  at  that  point,  as  in 
Fig.  6. 

Suppose  the  load  on  A  A'  to  be  uniform,  and  supported  by  rods, 
B  c  and  B'  c' ;  A  A'  not  to  be  continuous,  but  to  be  divided  at 
B  and  B'.  -This  corresponds  to  the  weight  on  c  and  c'  in  Fig.  12. 
If  the  beam,  A  A',  be  continuous  and  level,  then  ^  w  is  on  B  c  and 
B'  c',  and  -3^  on  A  and  A'.  This  is  safest  to  take,  being  greatest, 
though  it  is  not  generally  done.  In  either  case,  calling  w'  the  load 
on  B  c  or  B'  c',  then  the  horizontal  thrust  on  c  c'  and  the  pull  on 


on  c  A  and  c'  A'  =  w'  ^.    If  a  similar  load  were  on  top,  the 

stresses  would  be  the  same. 

When  a  bridge  of  this  form  is  reversed  the  stresses  remain  the 
same  except  that  the  former  stresses  of  compression  have  become 
extension,  and  vice  versa.  This  arrangement  may  be  extended  to 
any  number  of  panels.  It  is  preferable  for  materials,  like  wood 
and  wrought  iron,  because  the  shortest  pieces  are  exposed  to  com- 
pression. A  large  number  of  points  may  be  supported  in  the  same 
Avay. 

Suppose  a  uniform  load,  Fig.  13. 

w,  on  a  beam,  A  A',  Fig.  18.  f  D  E  D' 

Each  post  or  vertical  tie 
supports  i  w  =  w'.  The 
struts,  KB  and  EB'  resist  a 

stress  =  i  w'  ?^,  as  found 


APPENDIX   F.  435 

from  Fig.  6.  They  produce  a  horizontal  strain  at  K  and  on  B  B' 
=  i  w'  —  .  The  weight  on  D  or  D'  =  w'  +  i  V  =  |  w'  (i  w' 
being  transferred  from  E).  Consequently,  D  A  and  D'  A'  have  a 
stress  =  |  w'  ^?.  They  produce  a  horizontal  strain  on  D  D'  and 

A  A'  =  f  w'  ^?.     The  horizontal  strain  B  B'  =  the  sum  of  the  two 

D  B 


horizontal  strains  =  tt  W  +  f  w')  i  =  i 

So  proceed  for  any  number  of  panels.  It  will  be  found  that 
the  strains  on  the  posts  and  on  the  struts  increase  in  a  direct  ratio 
to  the  distance  from  the  centre.  Their  strength  and  size  should, 
therefore,  be  increased  in  the  same  ratio.  The  strains  on  the  top 
and  bottom  beams  increase  from  the  ends  to  the  middle,  but  not  in 
a  direct  ratio.  The  increase  is  most  rapid  as  you  proceed  from  each 
end,  and  becomes  less  rapid  on  approaching  the  centre  or  middle. 
It  is  analogous  to  that  of  a  solid  beam,  in  which  latter  case  the 
relative  increase  is  indicated  graphically  by  a  parabolic  curve. 

The  usual  formula  for  the  horizontal  stress  on  a  frame,  caused 
by  a  uniform  load  (£  w  —.  —  ),  supposes  the  weight  to  be  uniformly 

applied  at  the  ends  of  the  struts,  as  well  as  distributed  uniformly 
over  the  roadway.  This  is  the  case  in  frames  which  have  an  even 
number  of  panels;  but  is  not  so  with  those  of  an  uneven  num- 
ber. For  example,  with  three  panels,  the  horizontal  stress 

=  i  w  ffi1  ;     for    five    panels  ~  w  S-jg5  ;     for     seven   panels 

=  -y  w  —.—  ;     and  generally  for  n  panels   (n  being  uneven) 

(1  \       span 
»-8^')Wlfee- 

We  now  see  that  all  truss  bridges  are  composed  of  three  sys- 
tems or  sets  of  pieces  :  1.  Chords  of  stringers,  horizontal,  or  nearly 
so.  2.  Ties  or  posts,  vertical,  or  oblique.  3.  Struts. 

With  these  three  elements  bridges  may  be  constructed  of  several 
hundred  feet  span,  and  bear  safely  a  load  uniformly  distributed  : 
but  unless  very  heavy  they  will  not  bear  safely  a  partial  load. 


436 


APPENDIX   F. 


Counter-bracing.    A  bridge  uniformly  loaded  tends  to  assume 


Fig.  14. 


the  form  indicated  by 
dotted  lines  in  Fig.  14, 
in  which  the  rectangular 
panels  become  rhom- 
boids. This  tendency  is 
resisted  by  the  struts  which  must  be  compressed  or  broken  before 
this  tendency  can  be  carried  out. 

But  let  a  passing  load  be  at  some  point,  c,  of  the  bridge,  being 
supported  finally  by  the  points  A  and  B.  The  directions  of  its 
pressure  are  c  A  and  c  B,  and  the  force,  c  A,  tends  to  make  the 
bridge  rise  at  D,  and  to  -pig.  55 

assume  the  form  shown 
by  the  broken  lines  in 
Fig.  15.  The  struts  do 
not  resist  this  action,  for 
they  now  occupy  the  lorg 
diagonals.  This  tendency  must  be  resisted  by  fastening  the  ends 
of  the  struts  to  the  chords,  or  putting  tie-rods  beside  them,  or  as  is 
most  usual  by  counter-braces,  i.  e.,  braces  placed  in  the  other  diag- 
onals of  the  panels.  The  bridge  cannot  now  rise  as  indicated 
in  Fig.  15,  without  breaking  or  bending  these  counter-braces. 

This  counter-bracing,  therefore,  checks  the  up-and-down  vibra- 
tions of  a  bridge,  and  renders  it  stiff  against  passing  loads,  while 
the  main  braces  give  it  strength  to  bear  uniform  loads.  In  very 
heavy  bridges  their  weight  may  render  counter-bracing  unneces- 
sary. 

The  strain  on  a  counter-brace  equals  the  greatest  weight  which 
can  ever  press  upon  any  point  of  the  bridge,  multiplied  by  the 
length  of  the  counter-brace,  divided  by  its  height  In  a  railroad 
bridge  this  greatest  weight  would  be  the  load  on  a  pair  of  drivers 
of  an  engine.  On  a  common  road  bridge  it  would  be  the  greatest 
load  between  a  pair  of  posts."  This  system  of  counter-braces  was 
first  fully  carried  out  by  Colonel  Long. 

LONG'S  BRIDGE. 

The  joints  and  fastenings  are  simple,  the  strain  on  the  timber  is 
direct,  and  any  piece  can  be  easily  removed  and  replaced.  All  the 


APPENDIX  *.  437 

principal  pieces  are  of  timber.  In  very  long  spans,  struts  (called 
arch-braces)  are  placed  under  the  ends,  and  a  roof  truss  in  tho 
middle  of  each  truss,  or  a  pair  of  struts  and  a  straining  beam 
along  each  side. 

The  peculiarity  of  Long's  bridge  is  in  the  mode  of  keying  the 
counter-braces.  They  are  kej'ed  or  wedged  so  strongly  that  the 
string-pieces  are  constantly  pressing  against  them,  and  when  a  load 
comes  on  the  bridge  its  only  effect  is  to  relieve  the  counter-braces 
from  the  pressure  against  them  and  to  transfer  it  to  the  main  braces. 

Thus  there  is  no  more  strain  on  the  bridge  -when  fully  loaded 
than  when  unloaded ;  only  the  strain  is  on  different  parts.  The 
effect  of  this  mode  of  keying  is  the  same  as  if  the  string-pieces  had 
been  originally  curved  upward,  or  arched,  and  then  brought  down 
straight  by  weights  hung  to  them,  the  counter-braces  then  wedged 
tight,  and  finally  the  weights  removed. 

A  load  now  coming  on  the  bridge  puts  it  in  the  same  condition 
as  it  was  before  these  imaginary  weights  were  removed,  i.  e.,  it 
takes  the  strain  off  the  counter-braces.  There  is,  therefore,  a  con- 
stant pressure  which  makes  the  bridge  very  stiff. 

HOWE'S  BRIDGE. 

In  this  an  iron  rod  replaces  the  vertical  post.  These  bridges  are 
very  generally  used,  but  are  not  durable.  The  expansion  and  con- 
traction of  the  rods  strain  the  bridge  out  of  shape  and  require  con- 
stant screwing  up.  Extra  struts  at  the  end  are  usually  added, 
sometimes  extending  to  the  abutment  under  the  bridge.  An  im- 
proved form  of  angle  block  is  now  used  to  prevent  crushing  the 
lower  chord  by •  the  nut. 

McCALLTJJl'S    BRIDGE. 

Its  peculiarity  is  that  the  upper  chord  is  arched.  The  ends  are 
also  strengthened  by  struts,  or  "  arch-braces"  (so  called),  thrusting 
against  the  abutments.  This  bridge  is  very  stiff,  but  uses  much 
timber.  Altogether  it  is  one  of  the  very  best  railroad  bridges.  Its 
counter-braces  are  adjusted  by  screws.  Sometimes  iron  rods  are 
added  near  the  ends,  so  as  to  suspend  that  part  of  the  bridge. 


438  APPEXDIX   F. 

LATROBE'S  BRIDGE. 

In  this  bridge  two  systems  are  combined  :  viz.,  that  of  long  struts, 
transferring  the  "weight  directly;  and  that  of  struts  and  tie-rods, 
transferring  the  weight  indirectly.  The  advisability  of  any  such 
combination  is  questionable,  owing  to  the  impossibility  of  so  adjust- 
ing the  two  that  they  shall  bear  their  exact  proportions  of  the  load, 

CLASS  II. — The  oblique  pieces  aU  resist  extension. 

This  is  rarely  used  for  wooden  bridges  ;  chiefly  for  iron  bridges. 
Hall's  and  Pratt's  bridges  belong  in  this  class.  The  principle  is 
good ;  the  shorter  pieces  being  compressed  in  which  way  timbers 
resist  most  advantageously. 

In  calculating  the  stresses  on  oblique  ties,  we  apply  the  same 
formulas  as  for  struts.  The  strain  is  now  one  of  extension  instead 
of  compression.  For  a  pair  of  ties,  the  horizontal  strain  produced 

by  a  weight,  w  =  i  w 


•1  w 


depression 
length 
depression' 


CLASS  III.  —  TJie  oblique  pieces  are  alternately  compressed  and  extended. 

The  weight  is  transferred  to  the  abutments  indirectly. 

In  the  preceding  forms  the  ties  were  vertical  and  the  struts  in 
clined.    In  Fig.  16  both  ties  Fia  16 

and  struts  are  inclined. 
The  stresses,  however,  fol- 
low similar  laws.  With  a 
uniform  load,  \v,  such  as  its 

own  weight,  the  vertical  strain  increases  uniformly  from  the  middle, 
•where  it  equals  zero  toward  the  end  where  it  equals  |  w.    At  x' 

x" 

from  end,  or  x1'  from  middle,  it  equals  w  -  .     The  strain  on  any 

span 

diagonal  whose    middle  is  «"  from  the  middle    of  the  bridge 


span  depth  of  panel 

tre  =  i  w  —  -.  -  .    At  ;:ny  point  x'  from  middle  or  x"  from  end, 
rise 


APPENDIX   F.  439 

it  =  ?L  x  x  (span  ~  x"  \  diminishing  from  the  centre  to  the  enda 
&         span  x  depth 

in  the  ratio  before  shown  by  a  parabolic  curve. 

When  the  loads  are  applied  along  the  top  or  bottom,  or  along  both. 
The  distance  x'  and  x",  in  the  preceding  formulas,  are  measured 
to  the  tops  of  the  diagonals,  •when  the  load  is  attached  to  the  bot- 
tom of  the  beam ;  to  the  lower  ends,  if  it  be  on  the  top ;  and  to 
their  middle,  if  the  load  be  equally  on  the  top  and  bottom,  as  its 
own  weight 

Bridges  of  this  form  are  called  "Triangular  girders,"  or"  War- 
ren's," or  "  Neville's."  If  the  number  of  oblique  pieces  be  doubled, 
then  each  sustains  half  the  above  strains. 

TOWN'S  LATTICE. 

This  is  a  lattice  of  common  plank.  It  is  easily  made,  but,  though 
strong,  is  deficient  in  stiffness.  The  material  is  not  advantageously 
disposed,  too  much  of  it  being  near  the  "  neutral  axis."  It  soon 
gets  loose  and  sags,  or  twists  sidewise,  i.  e.,  buckles.  It  is  Some- 
times strengthened  by  long  struts  and  straining  beams,  or  by  arch 
ribs.  To  calculate  a  lattice  bridge,  consider  the  truss  a  solid  beam 
with  holes  cut  out  of  it  where  the  spaces  in  the  lattice  are. 

MISCELLANEOUS  DETAILS. 

1.  The  ratio  of  height  to  length.    This  is  important.     The  most 
economical  is  \.   Short  spans,  requiring  great  strength,  may  have  i. 
In  long  spans  this  would  give  the  wind  too  much  hold,  and  the 
sides  would  twist  or  buckle.     Then  for  great  strength  use  |  or  |, 
while  for  moderate  length  and  stress  -fV  may  do. 

2.  Horizontal  braces  or  sway-braces.    They  are  to  prevent  lateral 
flexure.     The  greatest  possible  strain  on  them  Fjg.  17. 

is  the  wind,  which  operates  as  a  uniform  load. 
They  are  shown  in  plan  in  Fig.  17. 

3.  Stiffening  the  sides.    When  the  roadway 

is  on  top  ("  Deck  bridges")  use  transverse  vertical  bracing,  extend- 
ing from  the  top  chord  of  one  truss  across  to  the  bottom  chord  of 
the  other  truss.  When  the  road  is  not  on  top,  extend  the  needle- 
Iteams  beyond  each  side  of  the  bridge,  and  brace  the  top  chord  from 
it ;  otherwise  make  gallows  frames. 


440  APPENDIX   F. 

4.  Wedc/ing  up  the  ends  of  tlie  lower  chords.    This  produces  an 
initial  strain  of  compression,  which  the  stress  of  the  load  must 
overcome  before  it  begins  to  bring  a  strain  of  extension  upon  this 
lower  chord.    The  lower  chord  then  acts  somewhat  as  an  arch. 
An  objection  is  that  it  makes  the  strength  of  th<5  bridge  depend 
upon  the  resistance  of  the  abutment. 

5.  Double  roadway.     In  important  bridges  it  is  best  to  have  each 
track  separate  to  prevent  a  one-sided  strain. 

6.  Durability.    An  uncovered  wooden  bridge  is  seldom  safe  for 
more  than  eight  or  ten  years.    If  covered,  sided,  and  well  painted, 
it  may  last  thirty  or  forty  years.    Some  have  been  used  fifty  or 
sixty  years. 

WOODEN  ARCH  BRIDGES. 

A  beam  resting  on  two  supports,  sustains  a  load  by  the  compres- 
sion of  its  upper  fibres,  and  the  extension  of  its  lower  fibres.  If 
we  confine  the  ends  of  the  beam  by  immovable  obstacles,  these  will 
be  substitutes  for  the  tension  of  the  lower  fibres,  which  may  there- 
fore be  removed  without  lessening  the  strength  of  the  beam,  as  may 
also  the  extreme  portions  of  the  upper  fibres.  So  too  a  board 
laid  on  two  supports  will  bear  a  certain  weight.  Bend  it  up  and 
confine  its  ends  and  it  will  bear  a  much  greater  weight.  This 
principle  may  be  adopted  in  building  bridges  of  considerable  span. 
Strong,  cheap  bridges  may  be  made  by  forming  an  arch  of  planks. 
One  such,  with  a  span  of  130  feet,  rise  14  feet,  was  formed  of  3" 
plank  in  15  layers  and  30"  wide.  Three  locomotives  on  it  caused 
a  deflection  of  only  $".  The  roadway  may  pass  either  over  the 
top,  resting  on  posts  and  struts,  or  be  at  the  springs  and  thus  act  as 
a  tie-beam,  beirg  suspended  from  the  arch.  It  is  then  called  a 
"  Bowstring"  bridge. 

Perhaps  the  strongest  and  cheapest  form  of  bridge,  where  abut- 
ments can  be  obtained,  would  be  a  parabolic  arch,  increasing  in 
cross-section  from  crown  to  spring,  according  to  stress,  and  stiff- 
ened by  counter-bracing.  The  counter-braces  may  be  wedged 
down,  as  in  Long's  bridge,  and  thus  made  very  stiff,  as  well  as 
Btrong. 

Double  or  parallel  arches  are  always  bad.  Suppose  the  "  neutral 
axis"  to  pass  near  the  middle  of  the  lower  arch  rib.  Only  half  the 


APPENDIX  F.  441 

strength  of  the  timber  is  used,  being  the  upper  portion  of  the  upper 
arch  rib,  and  the  extreme  portion  of  the  lower  arch  rib.  The  Erie 
Railroad  Cascade  Bridge  was  built  on  this  plan.  Span,  275  feet ; 
rise,  45  feet 

Combination  of  an  arcli  and  truss.  This  is  much  used,  and  its 
expediency  is  advocated  by  some  eminent  engineers.  There  are, 
however,  grave  objections.  It  is  impossible  so  to  combine  them 
that  the  arch  and  truss  shall  each  bear  its  due  share  of  the  pres- 
sure. One  will  give  way  before  the  pressure  comes  on  the  other. 
One  of  the  best  combinations  is  Burr's  bridge.  The  relative  stress 
on  the  arch  and  truss,  of  a  combination,  maybe  so  adjusted  by  set- 
screws  as  to  throw  any  desired  portion  of  the  stress  upon  either 
the  arch  or  the  truss;  but  this  ratio  will  be  changed  by  eveiy 
passing  load,  and  by  every  change  in  the  temperature 

It  an  arch  be  used,  and  the  abutments  will  allow,  it  is  best  to 
depend  for  the  whole  strength  upon  it,  and  to  employ  a  truss 
merely  to  stiffen  it. 

Wooden  Suspension  Bridges.  Wood  is  rarely  employed  in  this 
way,  notwithstanding  its  greater  strength  to  resist  extension  than 
compression,  because  of  the  loss  of  material  caused  by  the  neces- 
sary bolts  and  straps.  A  bridge  on  this  plan  was  built  by  Burr 
across  the  Mohawk  at  Scheuectady,  N.  Y.,  hi  1808,  and  is  still 
(1871)  in  use. 

Lake's  Bindge.  This  is  a  combination  of  a  wooden  arch  and 
suspension  bridge.  Fig.  18.  A  timber  is  sawn  nearly  through 
lengthwise,  its  ends  con- 
fined,  and  the  middle  por- 
tions are  wedged  apart. 
It  will  now  bear  a  much 
greater  load  than  before. 
Two  timbers  may  be  thus 
combined.  For  great  spans,  the  upper  and  lower  portions  may  be 
formed  by  splicing  timbers.  The  principle  is  good.  It  is  recom- 
mended for  military  bridges. 

Wooden  bridges  have  been  extensively  used  in  this  country,  on 
account  of  their  cheapness ;  timber  being  plenty  and  capital  limited. 
They  are,  however,  faulty  from  their  elasticity  and  consequent 
vibration,  and  their  perishable  nature. 
19* 


442  APPENDIX  F. 

Iron  bridges  are  employed  with  great  success,  and  their  use  is 
increasing.  They  have  the  requisite  rigidity;  and  although  the 
first  cost  is  greater  than  for  wooden  bridges,  their  imperishable 
nature,  if  well  cared  for,  renders  them,  in  a  majority  of  cases,  most 
economical. 

IRON  BRIDGES. 

They  are  divided,  like  wooden,  into  Trabeate,  Arcuate,  and  Sus- 
pension. The  stresses,  strains,  and  calculations  are,  of  course,  the 
same  for  them  as  for  wooden  bridges ;  only  using  the  experimental 
coefficient  of  strength  for  iron,  cast  or  wrought,  instead  of  that  for 
wood. 

CLASSIFICATION. 

I.  TRABEATE. 

1.  Cast  iron  girders. 

Simple  girders.    Built  girders.    Trussed  girders. 

2.  Wrought  iron  girders. 

I-shaped  beams.    Box  or  tubular  girders. 

3.  Wrought  iron  truss  work. 

Post's,  Fink's,  Bollman's,  Whipple's,  Rider's,  Heath  s, 
etc.,  etc. 

1    TRABEATE  IRON  BRIDGES. 
1.   CAST  IRON  GIRDERS. 

Relative  strength  of  cast  iron  beams.  Fig.  19  (a)  is  a  cross-section 
of  a  beam  made  by  Boulton  &  Watts  in  1801.  It  was  improved 
by  Fairbairn  in  1825,  the  vertical  rib  being 
made  thinner  and  the  lower  flange  thicker  (6). 
Tredgold's  beam  (c)  has  equal  upper  and 
lower  flanges.  The  strongest  form  is  Hodg- 
kinson's  (d),  the  lower  flange  being  six  times 
the  upper  one.  The  relative  strength  of  these 
beams,  Hodgkinson's  being  taken  as  unity, 
is :  Boulton  &  Watts',  0.51 ;  Fairbairn'8, 0.75 ; 
Tredgold's,  0.62 ;  and  Hodgkinson's,  1. 

For  short  distances,  a  single  girder  may  be  used  for  each  rail. 
For  30  or  40  feet,  use  two  girders  on  each  side,  with  a  timber  be- 
tween them  to  carry  the  rail. 


APPENDIX   F.  443 

The  greatest  possible  load  should  not  exceed  one-sixth  the 
breaking  weight  The  test  load  should  be  about  twice  the  greatest 
load,  or  about  one-third  the  breaking  weight.  The  deflection  un- 
der the  permanent  load  should  not  be  more  than  j^c  of  the  length. 
A  "  camber"  of  1  in  300  should  be  used.  One  girder  76  feet  long 
has  been  cast. 

Built  girders.  For  spaces  too  long  for  simple  girders,  built 
girders  are  used,  fitted  closely  at  the  joints  with  flanges  there 
bolted  together.  Spans  of  120  feet  have  been  thus  crossed. 

Fig.  20. 
A; C A  Fig.  21. 

Trussed  girders.  Cast  iron  beams  sometimes  have  wrought  iron 
tension  rods  applied  to  them,  as  in  Figs.  20  and  21,  with  the  object 
of  strengthening  the  lower  flange ;  the  two  rods  helping  it  to  resist 
extension.  The  rods  are  tightened  by  screws  or  wedges,  so  as  to 
have  an}'  amount  of  initial  tension  in  advance;  but  it  is  difficult 
so  to  adjust  the  two,  that  each  shall  bear  its  share  of  the  strain ; 
and  even  if  this  adjustment  were  once  made  it  would  be  altered 
after  any  strain,  owing  to  the  different  "  sets"  of  wrrought  iron  and 
cast  iron.  Since  for  respective  stresses  equal  to  %  breaking  weight 
for  each  (say  5  tons  per  square  inch  for  cast  iron  and  15  tons  for 
wrought),  the  elongation  for  wrought  iron  is  2^  times  that  of  cast, 
and  its  set,  10  tunes  as  great  as  that  of  cast.  This  adjustment,  and 
with  it  the  strains  coming  on  each,  would  also  vary  with  every 
change  of  temperature,  since  wrought  iron  expands  with  heat  more 
than  cast  iron.  The  combination  is  therefore  bad.  Cast  iron  is 
never  safe  for  girders ;  wrought  iron  should  be  used. 

Wrought  iron  bridges.  The  resistance  of  wrought  iron  for  rail- 
road bridges  is  safely  8600  pounds  per  square  inch,  or  about  |  of 
its  breaking  weight  For  common  road  bridges,  11,400  pounds. 
These  are  safe  limits.  In  England,  11,400  is  used  for  railroads,  and 
18,000  for  cast  iron.  The  greatest  possible  load  for  an  iron  rail- 
road bridge  is  in  Austria  called  2800  per  rmning  foot  for  each 
track ;  in  Russia,  1600 ;  in  France,  2700 ;  in  England,  2300  to 
«UOO, 


<M4  AP'PEKDIX  F. 

The  proper  trial  load  may  be  from  40  to  80  pounds  per  square 
foot  of  roadway,  according  to  the  probabilities  and  importance  of 
the  bridge. 

In  France,  iron  railroad  bridges  are  by  law  tested  thus:  For 
spans  under  64  feet,  3300  pounds  per  running  foot ;  and  for  spans 
over  that,  2640  pounds  per  running  foot  is  used ;  but  the  load  in 
this  last  case  must  be  at  least  200,000  pounds. 

Wrought  iron  resists  extension  much  more  than  compression, 
therefore  the  compressed  parts  of  wrought  iron  beams  (the  upper 
flange  of  a  beam  supported  at  both  ends)  should  be  nearly  as  2:1. 
They  are  usually  made  nearly  the  same-,  since  for  small  strains  its 
resistances  are  about  the  same. 

Bridges  of  I-shaped  beams.  Up  to  2£  feet,  a  single  rail  would 
answer.  From  that  to  five  feet,  double  rails,  bolted  to- 
gether  by  the  lower  flange.  A  common  form  for  a 
wrought  iron  girder  is  shown  in  Fig.  22.  The  dimen- 
sions will,  of  course,  depend  on  the  span.  The  usual 
ratio  of  depth  to  span  is  about  1  to  14.  Parabolic 
girders  have  been  used. 

Box  or  tubular  girders.  The  ultimate  tenacity  of  plate 
girders  with  double  riveted  covering  plates,  is  45,000  pounds  per 
square  inch  of  cross-section.  The  ultimate  resistance  to  crushing 
is  36,000  pounds  per  square  inch.  One  such  bridge  has  a  span  of 
150  feet,  the  girders  being  12  feet  high  and  3  feet  wide. 

Another,  of  two  tubular  beams,  of  170  feet  span,  weighed  130 
tons,  gross,  and  cost  $100  per  ton,  equals  $76  per  foot.  Another, 
of  one  girder  of  76  feet  span,  cost  $100  per  ton,  and  $42  per 
foot. 

When  the  beams  are  small  and  liable  to  give  way  by  bending, 
use  the  formula  for  wrought  iron  posts.  When  the  thickness  of 
the  plates  is  not  less  than  •&,  the  diameter  of  y\s.  33. 

a  square  tube,  the  ultimate  resistance  of  it  to 
buckling  or  bending  is  27,000  pounds  per 
square  inch  of  the  cross-section.  Fig.  23 
shows  the  common  form  of  tubular  girders. 
For  small  spans  each  line  of  rail  rests '  on  a 
tube.  For  greater  spans,  each  line  of  rails 


APPENDIX  F.  445 

•will  have  a  pair  of  them.  For  still  greater  spans,  the  roadway 
may  go  through  the  tube.  For  example,  the  Britannia  bridge. 

The  Britannia  tubular  bridge,  over  the  Menai  Straits,  has  two 
spans  each  of  460  feet,  and  two  of  250,  its  total  length  being  1500 
feet.  Its  tubes  are  30  feet  high  and  14  wide.  Its  top  and  bottom 
are  cellular,  being  composed  of  two  parallel  sheets,  18  inches  apart, 
and  connected  by  cross-plates  which  form  a  series  of  square  cells 
or  tubes.  The  material  is  boiler  iron,  from  f  to  $  inch  thick,  in 
sheets  united  by  two  million  rivets,  and  stiffened  by  sixty-five  miles 
of  angle  iron.  Heavy  trains  daily  cross  it,  with  scarcely  percep- 
tible vibration.  But  its  cost,  $2,500,000,  must  always  render  it 
more  a  subject  of  admiration  than  of  imitation. 

The  Victoria  bridge  at  Montreal  is  on  the  same  plan.  The  centre 
span  is  330  feet,  and  12  spans  on  each  side,  each  242  feet  The 
plates  of  tubular  bridges  should  vary  in  thickness  in  the  same  ratio 
as  the  chords  and  braces  of  truss  bridges. 

TRUSS  WORK. 

Eider's  truss.    This  is  Long's  bridge  in  iron. 

Heath's  strut  truss.  This  is  built  of  sheet  iron,  stiffened  by 
T  irons. 

NOTE. — For  a  discumon  of  the  comparative  merits  of  the  Fink,  Bollman, 
Jones,  Mnrphy-Whipple,  Post,  Triangular,  and  Linville  trusses,  see  Col.  Merrill 
on  "Iron  Truss  Bridges  for  Railroads." 

Triangular  girders.  On  this  plan  is  Brunei's  "  Crumlin  Via- 
duct." It  has  10  spans  of  150  feet  each.  Each  span  composed  of 
nine  equilateral  triangles  15  feet  high.  Piers  200  feet  high,  of  cast 
iron  columns  strongly  tied  together. 

The  best  angle  for  the  struts  and  ties  is  45°.  Depth  usually  -^ 
to  -^  the  length. 

Lattice  bridges.  In  a  good  one  of  six  spans,  each  90  feet  in  clear, 
the  height  was  10  feet.  The  angles  were  45°.  Width  of  upper  and 
lower  stringers  was  10".  Thickness  2|",  made  of  three  bars  super- 
imposed. Lattice  bars  3£"  broad  and  $•"  thick.  Distance  apart 
from  centre  to  centre  13".  Riveted  at  eveiy  crossing.  Distance 
from  rivet  to  rivet  was  18".  The  objection  to  these  bridges  is,  that 
they  are  liable  to  buckle.  There  is  considerable  competition  be- 
tween the  advocates  of  these  and  boiler-plate  bridges. 


.*u  APPENDIX  F. 

II.    ARCUATE  IRON  BRIDGES. 

1.  Cast  iron  ^rch.  This  is  the  strongest  of  all  forms  of  cast  iron 
bridges.  Whipple's  arch  truss  is  one  of  this  class. 

An  arch  formed  of  cast  iron  tubes,  through  •which  the  water 
passes,  serves  as  both  a  bridge  and  conduit  on  the  "Washington 
Aqueduct.  Span  200',  rise  20',  diameter  of  tube  4  feet 

Wrought  iron  arches  are  usually  of  the  bow-string  form. 

The  steel  arch  bridge  across  the  Mississippi,  at  St.  Louis,  is  to 
have  three  spans,  the  middle  one  being  515  feet. 

Lave' s  form.  The  greatest  one  is  Brunei's  Saltash  bridge.  It 
has  two  spans  of  445  feet  each. 

SUSPENSION  BRIDGES. 

Various  plans  are  proposed  for  stiffened  suspension  bridges  for 
railroads ;  among  them  are  these  : 

1.  Adding  a  heavy  and  stiff  platform. 

2.  Connecting  a  truss  with  the  chain.   (Niagara.) 

3.  Making  the  chain  itself  a  truss.    (See  Latham,  plate  II.) 

4.  Suspending  many  points  of  the  platform  directly  from  the 
piers.     (Dredge's  plan.) 

5.  Sustaining  the  bridge  and  load  as  in  Bollman's  bridge,  the 
rods  themselves  being  supported  by  a  chain.    (Ordish's  plan.)    See 
Latham,  plate  VI. 

6.  Applying  stay  rods.    (Niagara.) 

Comparison  of  a  suspension  bridge  and  a  girder.  Suppose  them 
each  of  400  feet  span  and  40  feet  deep.  The  weight  of  a  chain  of 
proper  strength  would  be  about  260  tons.  The  weight  of  a  girder 
of  equal  strength  would  be  about  900  tons.  Under  a  stationary 
load,  (he  former  would  deflect  about  twice  as  much  as  the  latter. 
Under  a  moving  load,  such  as  would  cause  a  wave  of  2  feet  on  the 
former  and  3  inches  on  the  latter,  the  shock  to  the  structures  would 
be  128  limes  as  great  on  the  suspension  bridge  as  on  the  other. 
Also  oscillations  tend  to  accumulate  on  the  suspension  bridge. 

Sections  to  give  the  chains.  The  French  government  rule  is  this: 
On  trials,  apply  40  pounds  per  square  foot  of  platform.  The  ten- 
•ion  shall  not  exceed  for  bar  iron  ^,  and  for  wire  \  the  breaking 
weight,  which  is  a  tension  corresponding  to  about  17,000  pounds 


APPENDIX   F.  447 

and  26,000  pounds  per  square  inch  respectively.  The  strain  of  the 
unloaded  bridge  is  about  i  this. 

Roebling  allows  7  wires  of  i"  diameter  for  each  ton  of  maximum 
tension,  equivalent  to  320  pounds  per  wire,  or  $  the  breaking 
weight.  The  constant  load  is  i  breaking  weight.  The  vertical 
suspending  rods  are  loaded  to  only  -^  breaking  weight,  being  ex- 
posed to  shocks.  The  weight  of  the  cable  increases  as  the  square 
of  the  span. 

Possible  length.  They  might  be  built  of  one  mile  length  or  span. 
For  example,  a  No.  10  wire  will  support  safely  a  strain  of  500 
pounds,  its  breaking  weight  being  three  or  four  times  that.  Such 
a  wire  suspended  over  a  span  of  4000',  •with  a  versed  sine  of  500', 
would  have  a  tension  of  only  212  pounds,  or  £  breaking  weight. 
Such  a  wire  would  bear  its  own  weight  across  a  span  of  three 
miles,  with  a  versed  sine  of  -fa  that. 

The  East  River  Suspension  Bridge,  connecting  New  York  and 
Brooklyn,  is  to  have  a  single  span  of  1600  feet. 


STONE   BRIDGES. 

The  bridges  necessary  on  railroads,  when  of  stone,  present  pecu- 
liar difficulties  in  their  construction.  This  is  owing  .to  the  fre- 
quently unavoidable  flatness  of  the  arches  (a  characteristic  which 
it  is  not  easy  to  unite  with  sufficient  strength,  both  in  reality  and  in 
appearance),  and  to  the  obliquity  with  which  they  often  cross  other 
roads,  and  which  compels  the  employment  of  "skew-arches," 
which  require  more  than  ordinary  skill  in  both  the  engineer  and 
the  builder. 

MOVABLE  BRIDGES. 

L  Turning  bridges. 

1.  Turning  on  one  end. 

2.  Turning  on  the  centre,  or  pivot  bridges. 
II.  Lifting  bi~idges. 

III.  Sliding  bridges.  . 

1.  Raise  or  lower  one  end  of  the  draw,  and  shove  it  back 
on  rollers. 


448  APPENDIX   F. 

2.  Shove  the  roadway  sideways,  to  m«iV;»  room  to  shove 

the  draw  back. 

3.  Shove  the  draw  sideways  and  then  ran  it  back. 
IV.  Floating  bridges. 

1.  Boat  bridges. 

2.  Pontoon  bridges. 


APPENDIX  G.  449 


APPENDIX 


SPECIFICATIONS. 

IN  making  out  specifications  for  the  execution  of  any  work, 
everything  should  be  plainly  expressed  and  nothing  left  to  be 
inferred. 

SPECIFICATIONS  FOR  GRADING. 

1.  DESCRIPTION  OF  THE  WORK. 

This  usually  refers  to  the  maps  and  plans  defining  the  centre 
line,  cross-section,  true  grade,  and  sub-grade.  Grade  is  the  top  of 
the  bank,  as  completed  and  ballasted.  Sub-grade  is  from  one  to 
two  feet  below  this.  It  is  the  top  surface  of  the  earthwork  before 
the  ballast  is  put  on. 

2.  PRELIMINARY  WORK. 

Clearing.  All  trees,  logs,  brush,  and  other  vegetable  matter  to  be 
removed  from  the  ground  oh  which  the  banks  are  to  be  placed. 

Grubbing.  All  stumps  and  large  roots  to  be  grubbed  out,  the 
entire  width  of  the  work. 

Mucking.  All  soft  earth  to  be  removed  down  to  two  feet  below 
sub-grade. 

3.  EXCAVATION. 

All  the  dimensions  should  be  given,  i.  e.,  width,  side  slopes,  etc. 
Also  the  distance  below  grade  to  which  the  excavation  is  to  be 
made  to  allow  for  ballasting.  Ditches  must  be  cut  along  the  top 
of  the  slope  to  protect  the  slopes  of  the  cut.  Their  size  to  depend 
on  how  much  will  be  required  of  them. 

Classification.  One  railroad  divides  the  material  only  into  earth 
and  rock,  the  former  including  everything  except  rock  in  ledges  or 
boulders  measuring  more  than  10  cubic  feet. 

Another  road  divides  it  into  earth  (including  "  hard-pan"  and 
stones  less  than  1  cubic  yard),  loose  rock  (comprising  detached  stones 


450  APPEHDIX    G. 

of  1  cubic  yard  and  over),  and  solid  rock  (embracing  all  rock  in 
ledges). 

Another  road  lias  also  three  classes:  solid  rock,  or  that  requiring 
blasting ;  soft  or  rotten  rock,  requiring  the  bar  and  pick,  but  not 
blasting ;  and  earth.  Detached  stones  less  than  3  cubic  feet  come 
in  the  last  class ;  and  those  between  3  and  20  cubic  feet  in  the 
second  class. 

On  the  Erie  Canal  enlargement  the  classes  were :  common  earth, 
hard-pan,  quicksand,  slate  rock,  and  solid  rock. 

How  measured  and  paid  for.  Excavation  is  sometimes  paid  for 
in  the  cut,  and  sometimes  in  the  bank. 

The  average  7iaul  should  be  named ;  also  the  distance  beyond 
which  extra  hauling  is  paid  for.  On  one  road  this  limit  was  1500 
feet,  and  beyond  that  the  contractor  was  paid  £  ct.  per  yard  per 
hundred  feet.  On  another  road  the  "  haul"  was  1000  feet,  and  the 
contractor  received  1  ct.  per  yard  for  eveiy  additional  hundred  feet. 

Usually  the  grade  is  so  established  as  to  make  the  "  cut''  and 
"  fill"  nearly  balance,  and  the  whole  work  is  measured  in  the  cut 
and  is  paid  for  as  excavation  only,  unless  the  "  haul"  exceeds  the 
limit  named  in  the  specification,  in  which  case  the  extra  hauling 
is  paid  for.  In  case  the  cut  does  not  quite  make  the  fill,  the  extra 
material  is  measured  in  the  "borrowing  pit,"  so  that  all  earthwork 
is  measured  in  the  excavation. 

4.  EMBANKMENT. 

jyimensdons.    This  includes  width,  side  slopes,  etc. 
Material.    No  soft  mud,  muck,  or  vegetable  matter  allowed  in 
the  bank. 

Subsidence.    In  making  high  banks  in  the  usual  manner,  allow- 
ance must  be  made  for  settling,  and  the  banks  be  made  so  much 
higher  originally.    The  following  lias  been  used  :— 
For  banks    5  feet  high,    3  inches 
"        "      10    "      "        5      " 
"      20    "      "        8}    " 
"        M      28    •"      "      10      " 
"        "      35    "      "      11      " 
"        «      40    "      "      12      " 
For  intermediate  heights  allowance  is  made  in  the  same  proportion. 


APPENDIX    0.  451 

An  embankment  should  never  be  carried  up  to  any  piece  of 
masonry,  as  a  bridge  abutment,  by  dumping  from  the  top  of  the 
bank  in  the  usual  way ;  but  should  be  wheeled  in  and  rammed  in 
layers. 

5.  BALLAST. 

The  kind  of  ballast  to  be  used,  and  the  thickness,  must  be  named. 
If  of  gravel,  the  quality  ;  if  of  broken  stone,  the  kind  of  stone  and 
the  size  of  the  pieces.  It  is  measured  on  the  finished  work. 

6.  DETAILS. 

The  position,  size,  and  slope  of  the  ditches.  Providing  for  th« 
passage  of  roads,  both  public  and  private,  and  of  water-courses. 
Protecting  banks  from  the  action  of  water,  by  rip-rap,  slope  walls, 
piles,  etc.  Extra  excavations,  as  foundation  pits  for  bridges, 
stations,  etc.  Location  of  spoil  banks  and  borrow  pits. 

SPECIFICATIONS    FOR     MASONRY. 

A  full  description  of  the  work  should  be  given,  accompanied  by 
the  requisite  drawings.  It  should  also  be  distinctly  stated  what  are 
the  requirements  for  the  first,  second,  third,  and  fourth  class 
masonry ;  *.  e.,  the  size  of  the  stones  to  be  used,  manner  of  laying, 
arrangement  of  headers  and  stretchers,  kind  and  amount  of  dress- 
ing, thickness  of  mortar  joints,  quality  of  cement,  etc. 

CLASSrFICATION   ON   THE   CROTON  AQUEDUCT. 

1.  Cut  stone.    "  This  means  that  a  tooled  draft  H"  wide  shall  be 
cut  on  the  face  and  joints,  so  as  to  bring  the  stone  into  the  proper 
lines  and  angles.     The  face  that  shows  is  to  be  axed  down  fair  and 
even.     The  beds  and  end  joints  to  be  dressed  so  as  to  be  laid  to  a 
joint  not  more  than  W'-     The  rear  beds  and  joints  to  be  dressed 
parallel." 

2.  Well-hammered  work.    "  The  stone  is  to  be  taken  '  out  of 
wind'  and  dressed  with  hammer,  pick,  and  points,  so  as  to  admit 
of  beiug  laid  to  a  compact  joint,  not  more  than  f".     The  stones 
are  to  hold  their  full  size  for  half  their  length  from  front  to  rear, 
and  on  the  rear  to  be  at  least  £  as  wide  and  §  as  thick  as  on  the 
front.     The  face  is  to  be  fair  but  not  very  smooth." 


452  APPENDIX   G. 

3.  Bough-hamme.red  work.  "  This  means  that  the  stones  are 
to  be  dressed  and  formed  with  so  much  regularity,  as  will  admit 
of  their  being  laid  in  a  compact  and  substantial  manner  and  so  aa 
to  make  good  lined  work."  See  pp.  186  and  187. 

The  hydraulic  cement  used  should  be  fresh-ground.  The  usual 
proportion  of  sand  and  cement  for  cement  mortar,  is  one  part  of 
cement  to  two  of  clean  sharp  sand.  When  lime  is  used  in  the 
mortar,  the  usual  proportions  are,  one  part  of  cement,  two  of  lime, 
and  five  of  sand. 

RAILROAD  RESISTANCES. 

[NOTE  TO  PAGE  265.] 

The  axle  friction  is  directly  as  the  radius  of  the  axle,  and  inversely 
as  that  of  the  wheel.  Let  w'  equal  the  weight  resting  on  the 
wheels,  and  r  and  r'  the  radii.  Then  the  axle  friction  equals 

fw' T-  ;  in  which  /  =  the  coefficient  of  friction  =  .05  to  .017,  and 

-  =  -ij  to  -fa    As  a   mean  we  have  .035  w'  x  -fa  =  .0033  w'  or 

about  TO  o  W. 

The  rolling  friction  at  the  circumference  of  the  wheel  equals/  w, 
w  being  the  whole  weight,  and  £  averaging  .001,  that  is,  about, 
.001  of  the  whole  weight,  or  about  one-half  the  axle  friction. 

Both  combined  equals,  approximately,  3^  of  the  whole  weight. 
The  fraction  ^j  is  often  used  for  the  friction  and  the  other  resist- 
ances at  very  low  speeds,  at  which  they  are  veiy  small. 

The  friction  on  railroads  has  usually  been  determined  by  letting 
cars  run  down  a  steep  inclined  plane,  succeeded  by  a  level  or  an 
ascent,  until  they  are  stopped  by  friction. 

Let  w  =  the  weight  of  the  car,  h  =  the  vertical  descent  of  the 
inclined  plane,  7t'  =  the  vertical  ascent  of  the  succeeding  plane, 
x  =  the  distance  of  the  descent,  x'  =  length  of  the  ascent,  and 
/ae'the  coefficient  of  friction. 

Then  the  "  work'"  accumulated  in  descending  =wh.  The  work 
ddne  before  the  car  comes  to  rest  =:  fw  (x  +  x')  +  w  h'.  Equating 

these  two  expressions,  and  reducing,  we  get,  /=  —~/-    ^ tiie 


APPENDIX    G.  453 

second  plane  be  level,  this  becomes  /=  .     If  the  second 

x  +  tf 

plane  desend,  /  = ;. 

x  +  x 

Recent  experiments  indicate  that  the  friction  is  not  entirely 
independent  of  the  extent  of  the  surface  or  the  velocity,  but  that 
it  increases  somewhat  with  them  ;  and  under  great  pressures  it 
increases  somewhat  faster  than  the  weights,  owing  to  abrasion 
taking  place. 

The  resistance  of  tfie  air  is  found  thus  :  A  velocity  of  one  mile  per 

hour  =  $u  ft.  per  minute.     Then  the  formula,  s  =  — ,  becomes  for 

this  speed,  s  =  (£*)»  -*-  2  x  32  =0'.0334.  A  column  of  air  of  this 
height,  and  a  base  of  one  square  foot,  weighs  1  x  0.0334  x  0.08 
=  0.0027  pounds. 

[NOTE  TO  PAGE  269.] 

A  simple  formula  by  D.  Grooch  for  the  resistance  on  rail- 
roads is  this :  The  resistance  of  the  train  in  pounds  per  T  (ton) 
=  6  +  .03  (v'  —  10) ;  in  which  v'  is  the  velocity  in  miles  per  hour 
That  is,  6  Iba.  per  T  +  0.3  Ibs.  per  T  per  mile  per  velocities  beyond 
ten  miles  per  hour.  For  less  velocities  omit  the  second  term.  For 
the  engine  and  tender  take  twice  the  above,  i.  e. ,  in  pounds  per  T 
use  12  +  0.6  (v'  —  10). 

D.  K.  Clark's  formula.  He  considers  part  of  the  resistance  to  be 
:i  constant  quantity,  and  the  rest  to  vary  as  the  square  of  the  velo- 
city. He  gives  for  the  resistance  of  the  train  in  pounds  per  T 

V9  * 

6  +  — .  'For  the  engine  and  tender  take  the  above  amount  per 
T  for  them  as  carriages,  and  in  addition,  for  the  resistance  of  the 
machinery,  take  2  +  — —  pounds  for  each  ton  in  the  total  weight 

of  the  train,  engine,  and  tender. 

Recent  French  experiments  make  the  total  resistance  of  the 
train,  including  the  engine,  at  speeds  of  from  16  to  25  miles  per 
hour,  0.003  to  0.0045  of  the  whole  weight ;  from  25  to  37  miles 
per  hour,  from  0.0045  to  0.0085  of  the  whole  weight.  Excluding 
the  engine  and  tender,  it  was,  at  24  miles  per  hour,  0.004 ;  at  31  miles 
per  hour,  0.0060 ;  and  at  35  miles  per  hour,  0.008. 


454  APPENDIX   G. 

A| 

[NOTE  TO  PAGE  276.] 
Resistance  on  an  ascent  in  a  straiglit  line. 

The  friction  of  the  axle  and  of  the  wheel  is  now  reduced  in 
the  ratio  of  1  :  cosine  of  the  angle  of  the  slope  with  the  horizon ; 
but  this  difference  is  so  small  that  it  may  be  neglected.  The  resist- 
ance of  the  air  is  not  changed. 

The  new  resistance  of  gravity  equals  w  .  sin.  angle  of  slope;  or, 

rise 


near  enough,  w  .  tan.  angle  of  slope  =  w 


horizontal  distance ' 


Steep  grades  in  practice. 

The  Baltimore  and  Ohio  Railroad  has  grades  of  116  ft.  per  mile 
for  7  miles,  with  some  curves  of  600  ft.  radius. 

Ellet's  Mountain  Top  Track,  in  Virginia,  has  an  average  of  257 
ft.  per  mile  for  2  miles,  and  a  maximum  grade  of  296  ft.  per  mile. 

Near  Genoa  a  railroad  has  a  grade  of  147  ft.  per  mile  for  6  miles, 
with  a  maximum  of  185  ft. 

The  Austrian  Semmering  Railroad  has  a  grade  of  132  ft.  for 
several  miles,  with  an  average  of  113  ft.  for  13  miles,  and  curves  of 
660  ft.  radius. 

The  Copiapo  Railroad,  in  Chili,  has  a  grade  of  196  ft.  per  mile, 
for  17  mfles.  At  its  chief  incline  it  has  211  ft.  per  mile  for  23  miles. 

The  Mexico  and  Vera  Cruz  Railroad  ascends  7000  ft.  in  55  miles. 

The  railroad  over  Mount  Cenis  has  a  grade  of  440  ft.  per  mile  for 
\\  miles,  with  one  curve  of  139  ft.  radius.  Its  gauge  is  3.6  ft  It 
has  a  middle  line  of  rail,  gripped  between  two  horizontal  Vheels, 
to  get  more  adhesion. 

[NOTE  TO  PAGE  271.] 

Resistance  on  curves. 

There  is  a  three-fold  difficulty  in  determining  the  resistance  on 
curves,  viz.,  that  the  facts  are  few ;  that  those  we  have  are  deficient 
in  details  of  speed,  character  of  engine,  condition  of  track,  etc. ; 
and  that  we  do  not  know  what  allowances  we  should  make  for 
these  differences,  even  if  they  were  all  given.  The  French  engi- 
neers have  worked  out  elaborate  formulas  for  these  resistances, 


APPENDIX   G.  455 

but  they  are  less  valuable  practically  than  the  results  of  observa- 
tion. 

It  is  now  proposed  to  give  some  of  these  results,  and  to  reduce 
the  resistances  of  the  curves  to  their  equivalent  grades  and  Ibs.  per 
ton,  and  finally  to  the  equivalent  increase  of  distance :  this  last 
being  the  niost  important  point  for  the  purpose  of  equating  lines. 

It  will  be  assumed  that  the  resistances  of  curves  are  inversely 
proportional  to  their  radii,  or  directly  to  their  "  degree,"  which 
equals  5730  divided  by  the  radius  in  feet.  This  assumption  is  true 
hypothetically,  though  practically  the  sharper  curve  would  cause 
greater  proportional  resistance. 

No.  1.  Mr.  Latrobe's  experiments  in  1844,  on  the  Baltimore  and 
Ohio  Railroad,  indicate  that  a  curve  of  400  feet  radius  (14$°) 
doubles  the  resistance  as  compared  with  a  straight  and  level  line, 
for  an  eight-wheel  car  at  3£  miles  per  hour,  the  original  resistance 
being  7.5  Ibs.  per  ton.  Then  a  1°  curve,  or  5730  feet  radius,  would 
be  equivalent  to  a  resistance  =  7.5  -f-  14J  =  0.52  Ib.  per  ton,  or  to 

an  ascent  per  mile  =  0.53  x  p^  =  1.23  feet 

No.  2.  Mr.  Ellwood  Morris  considers  this  too  much,  and  re- 
gards a  1°  curve  as  equivalent  to  an  ascent  of  1  foot  per  mile. 
This  corresponds  to  0.42  Ib.  per  ton. 

No.  3.  On  the  Pennsylvania  Central  Railroad  (under  Mr.  Haupt) 
the  grade  was  reduced  on  curves  at  the  rate  of  0.025  foot  per  100 
feet  per  degree  of  curvature.  This  makes  a  1°  curve  =:  1.32  feet 
per  mile  =  0.56  Ib.  per  ton. 

No.  4.  Another  writer  says  he  finds  a  400  feet  curve  =  21  feet 
per  mile.  Then  a  1°  curve  =  1.47  feet  per  mile  =  0.62  Ib.  per  ton. 

No.  5.  Mr.  W.  C.  Young,  when  superintendent  of  the  Utica  and 
Schenectady  Railroad,  found  the  trains  to  increase  their  speed  very 
decidedly  on  passing  from  a  20  feet  straight  grade  to  a  level  curve 
of  700  feet  radius.  Then  a  1"  curve  gives  very  decidedly  less  resist- 
ance than  a  grade  of  2.4  feet  per  mile. 

Xo.  G.  On  the  New  York  and  Erie  Railroad,  a  curve  of  955  feet 
radius  causes  more  resistance  than  a  10  feet  grade.  Then  a  1" 
curve  would  cause  more  than  an  ascent  of  1.67  feet  per  mile,  or  0.7 
Ib.  per  ton. 

No.  7.     On  the  Virginia  Central  Railroad,  Mr.  Ellet  found  a  300 


456  APPENDIX  G. 

feet  curve  to  cause  more  resistance  than  58  feet  greater  grade,  or 
about  as  much  when  the  engine  flanges  were  oiled.  Then  a  1" 
curve  would  cause  more  than  a  3  feet  ascent,  or  more  than  1^  Ib. 
per  ton.  This  is  excessive,  but  is  partly  accounted  for  by  the 
length  of  the  wheel-base  of  the  engine.  The  exceedingly  small 
radius  also  removes  this  case  from  the  ordinary  category. 

I  will  now  reduce  the  above  resistances  to  the  equivalent  distances, 
taking  the  resistance  on  a  straight  level  road,  at  the  freight  speed 
of  12  miles  per  hour,  as  10i  Ibs.  per  ton,  which  is  equivalent  to  24 
feet  ascent  per  mile,  and  the  resistance  at  the  passenger  speed  of 
30  miles  per  hour  as  twice  this. 

The  different  resistances  of  curves  for  different  speeds  will  not  be 
taken  into  account,  for  want  of  data.  That  portion  of  it  due  to 
friction  is  the  same  at  all  velocities ;  but  that  due  to  concussion 
must  increase  as  the  square  of  the  velocity,  since  it  consumes  "Liv- 
ing force."  With  this  omission,  and  the  preceding  assumptions, 
we  make,  approximately,  the  resistance  caused  by  turning  a  com- 
plete circle,  or  360°  of  curvature,  equivalent  to  the  following  in- 
crease of  distances  on  a  straight  and  level  line. 

No.  1.  Thk  makes  360°  equivalent  to  a  grade  of  1.23  feet  per 
mile,  for  360  x  100  feet  =  6.8  miles,  or  8.3  feet  for  one  mile.  This 
is  equivalent  to  an  additional  distance  of  8.3  -*-  24  =  0.35  mile  at 
freight  speed ;  or  to  about  half  this,  or  0.18  mile,  at  passenger  speed. 
It  would  be  equivalent  to  about  half  a  mile  at  the  slow  speed  of 
the  experiment,  since  a  resistance  of  7.5  Ib.  per  ton  would  be  doub- 
led by  a  grade  of  17  feet  per  mile,  and  8.3  -H  17  =  0.48  mile.  The 
same  result  is  also  obtained  by  noticing  that  a  complete  circle  of 
400  feet  radius  is  2513  feet,  or  nearly  half  a  mile  long. 

No.  2.  This  makes  360°  equivalent  to  a  grade  of  1  foot  per  mile 
for  6.8  miles,  or  6.8  feet  for  one  mile :  which  is  equivalent  to  6.8  •+• 
24  =  0.28  mile  at  freight  speed,  or  0.14  at  passenger  speed. 

No.  3.  By  similar  reasoning,  this  gives  360*  =  9  feet  ascent  for 
one  mile  =  0.38  mile  at  freight  speed,  or  0.19  mile  at  passenger 
speed. 

No.  4.  This  makes  360°  =  10  feet  ascent  for  one  mile ;  or  0.43 
mile  at  freight  speed,  and  0.21  mile  at  passenger  speed. 

Nos.  5,  6,  7,  may  be  analyzed  in  the  same  manner. 

The  average  of  the  first  four  is  that  turning  860°  of  curvature  u 


APPENDIX  G.  457 

equivalent  to  the  funning  an  additional  distance  of  0.36  mile  at 
freight  speed,  or  0.18  mile  at  passenger  speed.  No.  5  agrees  with 
this ;  No.  6  gives  more,  and  No.  7  much  more. 

The  groat  disparity  between  the  proportional  resistances  of  curves 
at  low  and  high  speeds  would  be  lessened  by  taking  into  account 
the  increase  of  the  absolute  resistance  of  the  curves  at  high  speeds. 

Perhaps,  hi  ordinary  cases,  one- third  of  a  mile  per  360°  would  be 
about  a  fair  equivalent  in  equating  for  curves,  particularly  taking 
into  account  the  other  objections  to  them. 


[NOTE  TO  PAGE  146.] 

Staking  out  the  side-slopes.  The  "  line,"  which  has  been  so  often 
spoken  of,  is  the  centre-line  of  the  road— its  axis— and  the  stakes 
which  have  now  been  set  at  every  hundred  feet,  on  both  straight 
lines  and  curves,  have  marked  out  only  this  centre-line.  Before 
the  "  construction"  of  the  road  is  commenced,  other  stakes  must 
be  set  to  show  how  far  on  each  side  of  the  centre-line  the  cuttings 
and  fillings  will  extend.  The  data  required  are  the  width  of  the 
road,  the  depth  of  the  necessary  cuttings  or  fillings,  and  the  ratio 
of  the  side-slopes  to  unity. 

Assume  that  the  road  is  to  be  20  feet  wide,  the  slopes  2  to  1,  and 
the  cuttings  6  feet.  Add  half  the  bottom  width  to  twice  the  depth, 
and  the  sum  (10  +  2  x  6)  =  22,  is  the  "  distance  out"  from  the 
centre  stakes,  at  which  the  cutting  stakes  must  be  set.  They 
should  be  marked  "  6.  + ,"  or  "  Cut  6,"  and  be  driven  obliquely,  so 
as  to  point  in  the  direction  of  the  slope.  If  the  road  had  been  in 
filling,  the  "  distance  out"  would  have  been  the  same,  but  the 
stakes  would  have  been  marked  "  6.—,"  or  "  Fill  6." 

Staking  out  the  side-slopes  is  thus  seen  to  be  very  easy  when 
the  ground  is  level  in  its  cross-section.  But  when  it  is  side- 
long, farther  calculations,  or  repeated  trials  with  a  levelling  instru- 
ment, are  required  to  find  the  "  distance  out"  which  will  correspond 
to  the  height  of  the  ground  above  or  below  the  grade  line  at  that 
precise  distance  out.  Take  the  same  width  of  road-bed,  side-slopes 
and  depth  at  the  centre-line,  as  in  the  preceding  paragraph,  and 
suppose  the  work  to  be  in  excavation  and  the  ground  to  have  a 
sidelong  slope.  The  distance  out  from  the  centre  stake  to  the 
20 


453 


APPENDIX  G. 


stake  on  the  up-hill  side  -will  now  be  more  ftan  23  feet,  for  the 
ground  rises  in  that  direction. 

Estimate  by  eye  the  rise  from  the  centre  to  where  the  stake  is  to 
be  set,  add  it  to  the  centre  height,  and  calculate  the  distance  out,  as 
before,  by  multiplying  the  new  depth  (i.  e.,  the  depth  at  the  centre 
plus  the  estimated  rise)  by  the  side-slope,  and  to  the  product  add 
half  the  width  of  the  road-bed.  Find  the  height  at  this  distance  out 
with  the  levelling  instrument,  and  if  it  agrees  with  the  estimated 
height,  the  point  has  been  correctly  taken ;  if  not,  try  again,  until 
the  estimated  height  agrees  nearly  enough  with  that  found  by  the 
fnstrunient  (on  railroad  work,  usually  to  within  one-tenth).  On 
the  down-hill  side  the  distance  out  will  be  less  than  if  the  ground 
were  level.  It  is  estimated  in  a  similar  manner. 

In  staking  out  ground  for  an  embankment  the  same  method  is 
used.  A  rise  in  the  ground  will  now  decrease  the  height  of  the 
bank,  and  consequently  the  distance  out,  and  vice  versa. 

When  the  difference  in  heights  between  the  upper  and  lower 
side-slope  stakes  is  so  great  as  to  necessitate  changing  the  instru- 
ment in  setting  the  stakes  on  the  same  cross-section,  then  set  the 
stakes  on  one  side  of  the  line  for  several  stations,  and  then  change 
the  instrument  and  set  those  on  the  other  side. 

"  Cross-section  rods"  are  often  used  for  this  work.  See  Gilles- 
pie's  "  Levelling  and  Higher  Surveying,"  Fig.  53. 

A  general  formula  for  any  case  may  be  readily  investigated. 
Examining  first  the  up-hill  side,  and  calling  the  slope  of  the  ground 
m  to  1 ;  that  of  the  side-slopes  n  to  1 ;  the  desired  distance  from 
Fig.  24. 


the  bottom  angle  of  the  cutting,  d ;  and  the  height  of  the  ground 
above  thai;  bottom  angle,  h  •  we  obtain  (as  on  page  121), 


APPENDIX  G.  459 


If  h  =  6,  n  =  2,  and  m  =  10,  d  =  6  x  —  =  15.    Then  the  up-hill 

cutting  stake  will  be  10  +  15  =  25  feet  from  the  centre  stake. 
Examining  next  the  down -hill  side,  and  using  a  symmetrical 

notation,  we  have,  -  —  h' ,  whence,  cE  =  h' .     mn   .    Let 

n  m  m  +  n 

ft'  =  4,  n  =  2,  andm  =10,  <f  =  4  x  —  =  6.7,  and  the  "  distance 
U 

out"  of  the  down-hill  stake  will  be  10  +  6.7  =  16.7  from  centre. 

Cases  of  embankment  will  be  represented  by  the  above  figure 
inverted. 

Let  p  and  q  be  the  reciprocals  of  the  slope  ratios  fi.  e.,p  =  — , 

and  q  =  -  J ,  or  p  and  q  =  the  heights  divided  by  the  bases.    Then 

the  formulas  are  simplified,  and  become, 

h                          h' 
d  =  .  and  d'  = . 


Formulas  of  this  kind  are  seldom  used  in  practice.  Side-slope 
stakes  can  be  set  very  rapidly  by  the  method  of  repeated  triali, 
given  before. 


- 


TABLE  I.— SLOPES  U  to  1.— BASE  20. 


I 

1 

2 

3 

4 

5    |     6 

7 

8 

9     i    10 

1 

! 

0 

0.39 

0.81 

1.28 

1.78 

2.311     2.89 

3.50      4.15 

4.83 

5.55 

0 

0.80 

1.24 

1.72 

2.24     2.80J     3.39 

4.02,     4.68 

5.39 

6.13 

1 

9 

1.24 

1.70 

2.20 

2.74     3.31      3.92 

4.57     5.20 

5.98 

6.74 

9 

3 

1.72 

2.20 

•2.72 

3.28     3.87J     4.50 

5.17J     5.87 

ti.61 

7.39 

3 

4 

2.24 

2.74 

3.28 

3.85     4.4i)      5.11 

5.80      6.52 

7.28 

8.07 

4 

5     2.80 

3.31 

3.87 

4.46!     5.09i     5.76 

t>.-!l>      7.  -JO 

7.93 

8.80 

5 

6J     3.39 

3.92 

4.50|     5.111     5.70!     0.44 

7.17      7.1.2 

8.72 

9.55 

6 

7      4.021     4.57 

5.17 

5.80     6.46      7.17 

7.91 

8.68 

9.50 

10.35 

7 

8      4.68      5.2li 

5.87 

li..VJ      7.20      792 

8.68 

9.48 

10.31 

11.18 

8 

9      5.39 

5.98 

6.61 

7.28 

7.98 

8.72 

9.50 

10.31 

11.16 

12.05 

9 

10|     6.13 

6.74 

7.39 

8.07 

8.80 

9.55 

10.351   11.18 

12.05 

12.90 

10 

11      6.91 

7.54 

8.20 

8.91 

9.65 

10.42 

11.24     12.09 

12.98 

13.91 

11 

12      7.72 

8.37 

9.05 

9.78 

10.54 

11.33 

12.171   13.04 

13.94 

14.89 

12 

13 

8.57 

9.24 

9.94 

10.68 

11.46 

12.28 

13.13     14.02 

14.94 

15.91 

13 

14 

9.46 

10.15 

10.87 

11.63 

12.42 

13.26 

14.131   15.04 

15.98 

10.96 

14 

15 

10.391  11.09 

11.83 

12.61 

13.42 

14.28 

15.17    16.09 

17.05 

18.05 

15 

1: 

11.351  12.07 

12  831  13.03    14.46 

15.33 

16.24    17.18 

18.16 

19.18 

16 

IT 

12.351  13.09 

13.87    14.68    15.54 

16.42 

17.  351   18.31 

19.31 

20.35 

17 

18 

13.3'J    14.15 

14.94    15.78|   16.1)5 

17.55 

18.50!   19.48 

20.50 

21.55 

18 

19 

14.46 

15.24 

16.051  16.9l|  17.80 

18.72 

19.68    20.68 

21.72 

22,80 

19 

•20 

15.57 

16.37 

17.20    18.07|  18.98 

19.92 

20.91 

21.92 

22.98 

24.07 

20 

01]* 

3 

4        5 

6 

7 

8 

9 

10 

1 

11 

12    i    13 

,4 

15 

16 

JL 

18 

19 

20 

I 

0     6.31 

7.11       7.94 

8.81 

9.72 

10.67 

11.65 

12.67 

13.72 

14.81 

0 

1 

6.91 

7.72 

8.57 

9.46 

10.39 

11.35 

12.35 

13.39 

14.46 

15.57 

1 

2     7.54 

8.37 

9.24 

10.15 

11.09 

12.07 

13.09 

14.15 

15.24 

16.37 

2 

3     8.20 

9.05 

9.94 

10.87 

11.83 

12.83 

13.87 

14.94 

16.05 

17.20 

3 

4      8.91 

9.78 

10.68 

11.63 

12.61 

13.63 

14.68    15.78 

16.91 

18.07 

4 

5 

9.65 

10.54 

11.46 

12.42 

13.42 

14.46 

15.54    16.65 

17.80 

18.98 

5 

1 

10.42 

11.33 

12.28 

13.26 

14.28 

15.33 

16.42 

17.55 

18.72 

19.92 

6 

7 

11.24 

12.17 

13.13 

14.13 

15.17 

16.24 

17.35    18.50 

19.68 

20.91 

7 

8 

12.09 

13.04 

14.02 

15.04 

16.09 

17.18    18.31]   19.48 

20.68 

21.92 

8 

1 

12.98 

13.94 

14.94 

15.98 

17.05 

18.16    19.31    20.50 

21.72 

22.98 

9 

10 

13.91 

14.89 

15.91 

16.96 

18.05 

19.18    20.35 

21.55 

22.80 

24.07 

10 

11 

14.87 

15.87 

16.91 

17.98 

19.09 

20.24    21.42    22.65 

23.91 

25.20 

11 

13 

15.87 

16.89 

17.94 

J9.03 

20.17 

21.33    22.54    23.78 

25.05 

26.37 

12 

13 

16.91 

17.94 

19.02 

20.13 

21.28 

22.46    23.68    24.94 

26.24 

27.57 

13 

11 

17.98 

19.03 

20.13 

21.26 

22.42 

25,631  24.87 

26.15 

27.46 

28.81 

14 

13 

19.09|  20.17 

21.28 

22  .  42 

23.61 

24..  -:i    20.09 

27.39 

28.72J   30.09 

15 

16 

20-.  24 

21.33 

22.46 

23.63 

24.83 

26.071  27.35 

28.67 

30.02J  31.41 

16 

17 

21.42 

22  .  54 

23.68 

24.87 

26.09 

27.35!  28.65 

29.98 

31.35    32.76 

17 

18 

22.65 

23.78 

24.94 

26.15 

27.39 

28.67 

29.98 

31.33 

32.721  34.15 

18 

19 

23.91 

25.05 

26.24 

27.46 

28.72 

30.02 

31.35 

32.72 

34.13 

35.57 

19 

SO 

25.20 

26.37 

27.57 

28.81 

30.09 

31.41 

32.76 

34.15 

35.57 

37.04 

20 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

TABLE    I.— SLOPES  l\  to  1.— BASE  30. 


1 

i  ;  2 

3 

4 

5 

6 

7 

8 

9 

10 

1 

fa 

(*. 

0 

0  57j     1.19 

1.83 

2.52 

3.24 

4.00 

4.80 

5.63 

6.49 

7.41 

0 

1 

1  17 

1.80 

2.46 

3.17 

3.91 

4.69 

5.50 

6.35 

7.24 

s.n 

i 

2 

1.80 

2.44 

3.13 

3.85 

4.61 

5.41 

6.24 

7.11 

8.02 

8.96 

2 

3 

2.46 

3.13 

3.83 

4.57 

5.35 

6.17 

7.02 

7.91 

8.83 

9.80 

3 

4 

3.17 

3.85 

4.57 

5.33 

C.13 

6.96 

7.83 

8.74 

9.69 

10.67 

4 

5 

3.91 

4.61 

5.35 

6.13 

6.94 

7.80 

8.69 

9.61 

lo!57 

11.57 

5 

C 

4.  09 

5.41 

6.17 

6.96 

7.80 

8.67 

9.57 

10.52 

11.50 

12.52 

6 

7 

5.50 

6.24 

7.02 

7.83 

8.(i9 

9.57 

10.50 

11.46 

12.46 

13.50 

7 

8 

6  35 

7.11 

7.91 

8.74 

9.61 

10.52 

11.46 

12.44 

13.46 

14.  bi 

8 

9 

7.24 

8.02 

8.83 

9.69 

10.57 

11.50 

12.46 

13.46 

14.50 

15.57 

9 

10 

8.17 

8.90 

9.80 

10.67 

11.57 

12.52 

13.50 

14.52 

15.57 

16.67 

10 

11 

9.13 

9.94 

10.80 

11.69 

12.61 

13.57 

14.57 

15.61 

1(5.69 

17.80 

11 

12 

10.13 

10.96 

11  83 

12.74 

13.69 

14.67 

15.69 

16.74 

17.83 

18.96 

12 

i:t 

11.17 

12.02 

12.01 

13.83 

14.80 

15.80 

16.83 

17.91 

19.02 

20.17 

13 

14 

12.24 

13.11 

14.02 

14.96 

15.94 

16.96 

18.02 

19.11 

20.24 

21.41 

14 

15 

13.35 

14.24 

15.17 

16.13 

17.13 

18.17 

19.24 

20.35 

21.50 

22.69 

15 

If, 

14.50 

15.41 

16.35 

17.33 

18.35 

19.41 

20.50 

21.63 

22.80 

24.00 

16 

17 

15.69 

16.61 

17.57 

18.57 

19.61 

20.69 

21.80 

22.94 

24.13 

25.35 

17 

18 

16.91 

17.85 

18.83 

19.85 

20.91 

22.00 

23.13 

24.30 

25.50 

26.74 

18 

1!) 

18.17 

19.13 

20.13 

21.17 

22.24 

23.35 

24.50 

25.69 

26.91 

28.17 

19 

20 

19.46 

20.44 

21.46 

22.52 

23.61 

24.74 

25.91 

27.11 

28.35 

29.63 

20 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

1 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

1 

0 

8.35 

9.33 

10.35 

11.41 

12.50 

13.63 

14.80 

16.00 

17.24 

18.52 

0 

9.13 

10.13 

11.17 

12.24 

13.35 

14.50 

15.69 

16.91 

18.17 

19.46 

i 

2 

9.94 

10.96 

12.02 

13.11 

14.24 

15.41 

16.61 

17.65 

19.13 

20.44 

2 

3 

10.80 

11.83 

12.91 

14.02 

15.17 

16.35 

17.57 

18.83 

20.13 

21.46 

i 

4 

11.69 

12.74 

13.83 

14.96 

16.13 

17.33 

18.57 

19.85 

21.17 

22.52 

4 

5 

12.61 

13.69 

14.80 

15.94 

17.13 

18.35 

19.61 

20.91 

22.24 

23.61 

5 

6 

13.57 

14.67 

15.80 

16.96 

18.17 

19.41 

20.69 

22.00 

23.35 

24.74 

6 

7 

14.57 

15.69 

16.83 

18.02 

19.24 

20.50 

21.80 

23.13 

24.50 

25.91 

7 

rt 

15.61 

16.74 

17.91 

19.11 

20.35 

21.63 

22.94 

24.30 

25.69 

27.11 

8 

P 

16.69 

17.83 

19.02 

20.24 

21.50 

22.80 

24.13 

25.50 

26.91 

28.35 

9 

10 

17.80 

18.96 

20.17 

21.41 

22.69 

24.00 

25.35 

26.74 

28.17 

29.63 

10 

11 

18.94 

20.13 

21.  3s|  22.61 

23.91 

25.24 

26.61 

28.02 

29.46 

30.94 

11 

19 

20.13 

21.33 

22.57 

23.85 

25.17 

26.52 

27.91 

29.33 

30.80 

32.30 

12 

13 

21.35 

22.57 

23.83 

25.13 

26.46 

27.83 

29.24 

30.69 

32.17 

33.69 

13 

14 

22.61 

23.85 

25.13 

•Jli.41 

27.80 

29.19 

30.61 

32.07 

33.57 

35.11 

14 

15 

23.91 

25.17 

26.46 

27.80 

29.17 

30.57 

32.02 

33.50 

35.02 

36.57 

15 

If. 

25.24 

26.52 

27.83 

29.19 

30.57 

32.00 

33.46 

34.96 

36.50 

38.07 

16 

17 

26.61 

27.91 

29.24 

30.61 

32.02 

33.46 

34.98 

36.46 

38.02 

39.61 

17 

18 

28.02 

29.33 

30.69 

32.07 

33.50 

34.96 

36.46 

38.00 

39.57 

41.19 

18 

19 

29.46 

30.80 

32.171  33.57 

35.02 

36.50 

38.02 

39.57 

41.17 

42.80 

19 

20 

30.94 

32.30 

33.69   35.11 

36.57 

38.07 

39.61 

41.19 

42.80 

44.44 

20 

11 

12 

13 

14 

15 

16 

17 

18 

19 

30 

TABLE  III.— SLOPES  2  to  1.— BASE 


II  1 

2 

3 

456 

7         8 

9 

10 

1 

H 

1 

I 

fc 

0      0.40     0.84 

1.33 

1.88     2.47      3.11 

3.80      4.54 

5.33 

6.17      0 

0.81      1.28 

1.80 

2.37 

2.99 

3.65 

4.37 

5.13 

5.95 

6.81 

1 

-J 

1.26      U78 

2.32 

2.91 

3.55 

4.25 

4.99      5.78 

6.62 

7.51 

2 

•J 

1  .  80      2  .  32 

2.89 

3.5l!     4.17 

4.89 

5.65 

6.47 

7.33 

8.25 

3 

4 

2.37      2.91 

3.51 

4.15      4.64 

•  5.58 

6.37 

7.21 

8.10 

9.04 

4 

5 

2.99      3.55 

4.17 

4.84      5.55 

6.32 

7.13 

8.00 

8.91 

9.88 

5 

6 

3.05      4.  --'5 

'  4.89 

5.58      6.32 

7.11 

7.95 

8.84 

9.78 

10.76 

6 

7j     4.37      4.991      5.05 

6.37      7.13'      7.95 

8.81'     9.73 

10.69 

11.70 

7 

8      5.13      5.78        6.47 

7.21      6.00       6.64       9.73     10.C.7 

11.65     12.69 

8 

9      5.95      0.6.        7.33 

a.  10      e.9l!     9.78    10.6LI     n.05 

12.67 

13.73 

9 

10 

6.81      7.51 

6.25      9.04      9.66     10.  ',6 
1 

11.711     12.09 

13.73 

14.81 

10 

11 

7.73^     8.44 

9.21 

10.02    10.891   11.80 

J2.76J   13.78 

14.84 

15.95 

11 

13 
13 

8.69     9.43 
9.70    10.47 

10.22 
11.28 

!11.  06    11.95    12.89 
12.15    13.06    14.02 

13.88    14.91 
15.04     16.11 

lft.00 

17.21 

17.13 
18.37 

12 
13 

14 

10.76    11.55 

18.3H 

13.28    14.22 

15.21 

16.25 

17.33 

18.47 

19.651  ]4 

15 

11.8?    1-2.09 

13.55 

14.47    15.43 

16.44 

17.51 

18.62 

19.78 

20.99 

15 

Iti 

13.04    13.86 

14.76 

15.70    10.09 

17.73 

18.81 

19.95 

21.13 

22.37 

16 

17 

14.  25    15.11 

16.0-2 

10.99    16.00 

19.06 

20.17 

21.33 

22.54 

23.80 

17 

18 

15.51    16.3'.l 

17.33 

18.32    19.36 

20.44 

21.58 

22.71 

24.00 

25.28 

18 

19 

16.81    17.73 

18.69 

19.70    20.77 

21.88 

23.04 

24.25 

25.51 

2U.81 

19 

i  "" 

16.17    19.11 

20.10    21.13    22.22 

23.36 

24.54 

25.78 

27.06 

28.40 

20 

2 

3 

4 

5 

6 

7 

8 

9 

10 

__;   : 

1 

S     11    |   12 

13 

i    14       15       16       17       18 

19 

20   |  I 

5n  i              j 

1    *** 

0     7.06 

8.00       8.99,  10.02    11.11 

12.25 

13.42    14.67 

15.95 

17.281     0 

j 

7.73 

8  69       9.7C 

10.76 

11.88 

13.04 

14.23 

15.51 

1C.  81 

is.!?!    i 

3 

4 
5 

8.44 
9.21 
10.02 
10.89 

9.43      10.47    11.55 
10.22      11.S8    12.39 
11.07      12.15    13.26 
11.951     13.06    14.22 

12.69 
13.55 
14.47 
15.43 

13.88 

14.76 
15.70 
16.69 

15.11!   16.39 

10.0-2    17.3: 
16.99    18.32 
18.00    19.30 

17.73 
18.69 
15.70 

20.77 

19.11 

20.10 
21.12 
22.22 

2 

2 

5 

G 

11.80 

12.89      14.  OS 

15.21 

16.44 

17.73 

19.06    20.44 

21.88 

23.36 

6 

7 

1-J.77 

13.88]     15.0-( 

16.25 

17.51 

18.81 

20.171  21.58 

23.04 

24.54 

7 

8 

13.78 

14.91 

16.11 

17.33 

18.62 

19.95 

21.33    22.71) 

24.25 

25.78 

8 

9 

14.84 

16.00 

17.2 

16.47 

19.78 

21.13 

22.54 

24.00 

25.51 

27.00 

9 

10 

15.95 

17.13 

18.37    19.65 

20.99 

22.37 

23.80 

25.28 

26.81 

28.40 

10 

11 

17.11 

18.32 

19.58   20.89 

22.25 

23.65 

25.11 

26.62 

28.17 

29.78 

11 

1* 

18.32 

lji.55 

ao.a 

22.17 

S3.5J 

24.99 

26.47 

•Jr.  01 

29.58 

31.21 

12 

13 

19.58 

20.84 

22.  K 

23.51 

24.91 

26.37 

87.88 

29.43 

31.04 

32.69 

13 

14 

20.89 

22  17 

23.5 

24.89 

26.32 

27.80 

29  .  3: 

30.91 

32.54 

34.22 

14 

15 

22.25 

23.55 

24.9 

20.32 

87.78 

29.26 

30.84 

32  .  4  4 

34.10 

3S.8( 

15 

u 

23.63'  24.99 

20.37    27.80 

29  .  -.'.- 

30.81 

32.39 

34.02 

35.70 

37.43 

16 

17 

25.111  26.47 

27.  fit 

29.33 

30.84 

32.39 

34.00    35.65 

37.30 

39.11 

17 

18    26.02 

28.00     29.4: 

t   30.91 

32.44 

34.02 

35.65    37.33 

39.06 

40.84 

18 

19    28.17 

29.58 

31.0 

38.54 

34.11 

35.70 

37.36|  39.06!  40.81 

42.62 

19 

34 

29.78 

31.21 

•2.0! 

34.22   35.80 

37.43 

39.11 

40.84    42.62 

44.44 

20 

11 

12 

13 

14 

15 

16   1    17 

18 

19 

20 

1 

TABLE  IV.— SLOPES  2  to  1.— BASE  30. 


Ij 

I 

1 

2 

3 

4        5 

6 

7 

8 

9 

10 

1 

0 

0.58 

1.21 

1.89 

2.621     3.40 

4.22 

5.10      6.02 

7.00 

8.02 

0 

1 

1.18 

1.84 

2.54 

3.30     4.10 

4.95 

5.85J     6.80 

7.80 

8.85 

1 

2 

1.84 

2.52 

3.25 

4.02     4.85 

5.73 

6.65      7.63 

8.65 

9.73 

2 

3 

2.54 

3.25 

4.00 

4.80     5.65 

6.55 

7.51      8.51 

9.55 

10.65 

3 

4 

3.30 

4.02 

4.80 

5.63 

6.51 

7.43 

8.41      9.43 

10.51 

11.63 

4 

5 

4.10 

4.85 

5.65 

6.51 

7.41 

8.36 

9.36 

10.41 

11.51 

12.65 

5 

6 

4.95 

5.73 

6.55 

7.43 

8.36 

9.33 

10.36 

11.43 

12.55 

13.73 

6 

7 

5.85 

6.65 

7.51 

8.41 

9.36 

10.36 

11.41 

12.51 

13.65 

14.85 

7 

8 

6.80 

7.63 

8.51 

9.43 

10.41 

11.43 

12.51 

13.63 

14.80 

16.02 

8 

9 

7.80 

8.65 

9.55 

10.51 

11.51 

12.55 

13.65 

14.80 

16.00 

17.25 

9 

10 

8.85 

9.73 

10.65 

11.63 

12.65 

13.73 

14.85 

16.02 

17.25 

18.52 

10 

11 

9.95 

10.85 

11.80 

12.80 

13.85 

14.95 

16.10 

17.29 

18.54 

19.8^ 

11 

1-2 

11.10 

12.02 

13.00 

14.02 

15.10 

16.22 

17.39 

18.62 

19.89 

12 

13 

12.30 

13.25 

14.25 

15.30 

16.40 

17.54 

18.74 

19.99 

21.28 

22!  e: 

13 

14 

13.54    14.52 

15.54 

16.62 

17.74 

18.91 

20.13 

21.41 

22.73 

24.10 

14 

15 

14.84    15.84 

16.89 

17.99 

19.13 

20.33 

21.58 

22.88 

24.22 

25.62 

15 

u 

16.18    17.21 

ia.28 

19.41 

20.58 

21.80 

23.07 

24.39 

25.76 

27.18 

16 

17 

17.58    18.63 

19.73 

20.88 

22.07 

23.32 

24.62 

25.96 

27.36 

28.80 

17 

1(3 

1!) 

19.021  20.10 
20.52|  21.62 

21.22 
22.76 

22.39   23.62 
23.96!  25.21 

24.89 
26.51 

26:21 
27.85 

27.58 
29.25 

29.00 
30.69 

30.47 
32.18 

18 
19 

•20 

22.061  23.18 

24.36 

25.58 

26.85 

28.17 

29.54 

30.96 

32.43 

33.95 

20 

1        2 

3 

4 

5 

6 

7 

8 

9 

10 

Sill 

12 

13 

14 

15 

16 

17 

18 

19 

20 

1 

N 

'- 

0 

9.10 

10.22 

11.  id    12.62 

13.89 

15.21 

16.58 

18.00 

19.47 

20.99     0 

9.95 

11.10 

12.30    13.54 

14.84 

16.18 

17.58 

19.02 

20.52 

22.06      1 

» 

10.85 

12.02 

13.25!  14.52 

15.84 

17.21 

18.63 

20.10 

21.62 

23.18     2 

3 

11.80 

13.00 

14.25    15.54 

16.89 

18.28 

19.73 

21.22 

22.76 

24.36      3 

4 

12.80 

14.02 

15.30    16.62 

17.99 

19.41 

20.88 

22.39 

23.96 

25.58!     4 

5 

13.85 

15.10 

16.40    17.74 

19.13 

20.58 

22.07 

23.62 

25.21 

26.85 

5 

G 

14.95 

16.22 

17.54 

18.91 

20.33 

21.80 

23.32 

24.89 

26.51 

28.17 

6 

7 

16.10 

17.39 

18.74   20.13 

21.58 

23.07 

24.62 

26.21 

27.85 

29.54 

7 

i 

17.29 

18.62 

19.99   21.41 

22.88 

24.39 

25.96 

27.58 

29.25 

30.96 

8 

18.54 

19.89 

21.28   22.73 

24.22 

25.76 

27.36 

29.00 

30.69 

32.43 

9 

10 

19.84 

21.21 

22.63   24.10 

25.62 

27.18 

28.80 

30.47 

32.  Id 

33.95 

10 

11 

21.18 

22.58 

24.02   25.52 

27.06 

28.65 

30.30 

31.99 

33.73 

35.52 

11 

IS 

22.58 

24.00 

25.47   26.99 

28.55 

30.17 

31.84 

33.55 

35.32 

37.33 

12 

13 

24.02 

25.47 

26.96   28.51 

30.10 

31.74 

33.43 

35.17 

36.96 

38.80 

13 

14 

25.52 

26.99 

28.51    30.07 

31.69 

33.36 

35.07 

36.84 

38.65 

40.52 

14 

15 

26.06 

28.55 

30.10   31.69 

33.33 

35.02 

36.76 

38.55 

40.39 

42.28 

15 

16 

28.65 

30.17 

31.74   33.36 

35.02 

36.74 

38.51 

40.32 

42.18 

44.10 

16 

17 

30.30 

31.84 

33.43   35.07 

36.76 

38.51 

40.30 

42.13 

44.92 

45.96|  17 

18 

31.99 

33.55 

35.17    36.84 

38.55 

40.32 

42.13 

44.00 

45.91 

47.88 

18 

19 

33.73 

35.32 

36.96   38.65 

40.39 

42.18 

44.92 

45.91 

47.85 

49.84 

19 

35.52 

37.13 

38.80    40.52 

42.28 

44.10!  45.96 

47.88 

49.84 

51.85 

20 

11 

12 

13       14 

15 

16       17 

18 

19 

20 

14 


"FOURTEEN  WEEKS  "IN  NATURAL  SCIENCE 

TEE1    TRK-A.TISE    IN    EACH    BK,^ 

.  BQRMAN  STEELE,  A.M. 

WEEKS 
COUESES 


NATURAL  PHILOSOPHY, 
ASTRONOMY. 

CHEMISTRY, 

G-EOLOGY. 

These  volumes  constitute  the  most  available,  practical,  and  attractive  text-books  on 
the  Sciences  ever  published.  Each  volume  may  be  completed  in  a  single  term  of  study. 

THE  FAMOUS  PRACTICAL   QUESTIONS 

devised  by  this  author  arc  alone  sufficient  to  place  his  books  in  every  Academy  and 
Grammar  School  of  the  land.  These  are  questions  as  to  the  nature  and  cause  of  com- 
mon phenomena,  and  are  not  directly  answered  in  the  text,  the  design  being  to  test 
and  promote  an  intelligent  use  of  the  student's  knowledge  of  the  foregoing  principles. 

TO  MAKE  SCIENCE  POPULAR 

is  a  prime  object  of  these  books.  To  this  end  each  subject  is  invested  with  a  charm- 
ing  interest  by  the  peculiarly  happy  use  of  language  and  illustration  in  which  this 
author  excels. 

THEIR  HEA  VY  PREDECESSORS 

demand  as  much  of  the  student's  time  for  the  acquisition  of  the  principles  of  a  single 
branch  as  these  for  the  whole  course. 

PUBLIC  APPRECIA  TION. 

The  author's  great  success  in  meeting  an  urgent,  popular  need,  is  indicated  by  the 
fact  (probably  unparalleled  in  the  history  of  scientific  text-books),  that  although  the 
first  volume  was  issued  in  1867,  the  yearly  sale  is  already  at  the  rate  of 

F  O  It  T  Y        T  H  O  XT  S -A.  3ST  ID        "V  O  L  XT  3VT  E  S  . 

PHYSIOLOGY   AND  HEALTH, 

By  EDWARD  JARVIS,  M.D. 
ELEJIEXTS  OF  PHYSIOLOGY, 
PHYSIOLOGY  AND  LAWS  OF  HEALTH. 

The  only  books  extant  which  approach  this  subject  with  a  proper  view  of  the  true 
object  of  teaching  Physiology  in  schools,  viz.,  that  scholars  may  know  how  to  taka 
care  of  their  own  health.  The  child  instructed  from  these  works  will  be  always 


mm 


ECIS     0"WJST     POCTOIR- 

11  (f5onsidet|  the  Lilies." 

BOTANY. 

WOOD'S  AMERICAN  BOTANIST  AND  FLORIST. 

This  new  and  eagerly  expected  work  is  the  result  of  the  author's  experience  and 
life-long  labors  in 

CLASSIFYING    THE  SCIENCE  OF  BOTANY. 

He  has  at  length  attained  the  realization  of  his  hopes  by  a  wonderfully  ingenious  pro- 
cess  of  condensation  and  arrangement,  and  presents  to  the  world  in  this  single  modav 
ate-sized  volume  a  COMPLETE  MAJMCJAL. 
In  370  duodecimo  pages  he  has  actually  recorded  and  defined 

NEA  RL  Y  4,000  SPECIES. 

The  treatises  on  Descriptive  and  Structural  Botany  are  models  of  concise  statement, 
which  leave  nothing  to  be  said.  Of  entirely  new  features,  the  most  notable  are  the 
Synoptical  Tables  for  the  blackboard,  and  the  distinction  of  species  and  varieties  by 
variation  in  the  type. 

Prof  Wood,  by  this  work,  establishes  a  just  claim  to  his  title  of  the  great 

AMERICAN  EXPONENT  OF  BOTANY. 


And  Only  Thorough  and  Complete  Mathematical  Series. 


I3ST     THREE 


/.   COMMON  SCHOOL   COURSE. 

Da  vies'  Primary  Arithmetic.  — The  fundamental  principles  displayed  In 

Object  Lessons. 
Davies'  Intellectual  Arithmetic.— Referring  all  operations  to  the  unit  1  na 

the  only  tangible  basis  for  logical  development. 
Davies'  Elements  of  Written  Arithmetic. —A  practical  introduction  to 

the  whole  subject.    Theory  subordinated  to  Practice. 
Davies'  Practical  Arithmetic.*— The  most  successful  combination  of  Theory 

and  Pradice,  clear,  exact,  brief,  and  comprehensive. 

//.  ACADEMIC  COURSE. 

Davies'  University  Arithmetic.*— Treating  the   subject  exhaustively  an 

a  science,  in  a  logical  series  of  connected  propositions. 
Davies'  Elementary  Algebra.*— A  connecting  Ih^j,  conducting  the  pupil 

easily  from  arithmetical  processes  to  abstract  analysis. 
Davies'  University  Algebra.*— For  institutions  desiring  a  more  complete 

but  not  the  fullest  course  in  pure  Algebra. 
Davies'  Practical  Mathematics.- The  science  practically  applied  to  tl>« 

useful  arts,  as  Drawing,  Architecture,  Surveying,  Mechanics,  etc. 
Davies'  Elementary  Geometry.— The  important  principles  In  simple  form, 

but  with  all  the  exactness  of  rigorous  reasoning. 
Davies'  Elements  of  Surveying-.— Re-written  in  1S70.     The  simplest  and 

most  practical  presentation  for  youths  of  12  to  16. 

///.  COLLEGIATE  COURSE. 

Davios'  Bourdon's  Algebra.*— Embracing  Sturm's   Theorem,  and  a  most 

exhaustive  and  scholarly  course. 
Davies'  University  Algebra.*— A  shorter  course  than  Eourdon,  for  Instltu. 

lions  have  less  time  to  give  the  subject. 
Davies'  Legendre's  Geometry.— Acknowledged  OitonJy  satisfactory  treatise 

of  its  grade.    300,000  copies  have  been  sold. 
Davies'  Analytical  Geometry  and  Calculus.— The  shorter  treatises, 

combined  in  one  volume,  are  more  available  for  American  courses  of  study. 
Davies'  Analytical  Geometry.  1  The  original  compendiums,  for  those  de. 
Davies'  DifT.  &  Int.  Calculus.    '     siring  to  give  full  time  to  each  branch. 
Davies'  Descriptive  Geometry.— With  application  to  Spherical  Trigonome^ 

try,  Spherical  Projections,  and  Warped  Surfaces. 
Davies'  Shades,  Shadows,  and  Perspective.— A  succinct  exposition  ot 

the  mathematical  principles  involved. 
3>avies"  Science  of  Mathematics.— For  teachers,  embracing 

I.  GRAMMAR  OF  ARITHMETIC,  III.  LOGIC  AND  UTILITY  OP  MATHEMATICS, 

JL  OUTLINES  oi1  MATHEMATICS,          IV.  MATHEMATICAL.  DICTIONARY. 


KEYS  MAY  BE  OBTAINED  7BOK  THH  PUBLISHERS 

BY  TEACHERS  ONLY. 


^U  ^Uru   all  ^U;uwn 

^m»     *"  j  limn  mi  mil  mil  inn  IIIIIIIIIHIIIIIIIIIIIIIIIIIII  (HI  Illl  . 

A     000316667     5 

NATIONAL     "TJTQrrn  u  V      BTAJSJJAKJJ 

SERIES.        UlulUHIi    TEIT-BOOKS, 


"History  is  (Philosophy  teaching  by  Examples." 

THE  UNITED  STATES. 

MONTKITH,  author  of  the  National  Geographical  Series.  An  elementary  work 
upon  the  catechetical  plan,  with  Maps,  Engravings,  Mem oriter  Tables,  etc.  ""For 
the  youngest  pupils. 

2.  Willard's    School    History,  for  Grammar  Schools  and  Academic  classe*. 

Designed  to  cultivate  the  memory,  the  intellect,  and  the  taste,  and  to  sow  the 
seeds  of  virtue,  by  contemplation  of  the  actions  of  the  good  and  great. 

3.  Willard's    Unabridged    History,    for  higher  classes  pursuing  a  complete 

course.  Notable  for  its"  ~iear  arrangement  and  devices  addressed  to  the  eye,  with 
a  series  of  Progressive  Maps. 

4.  Summary  Of  American   History.    A  skeleton  of  events,  with  all  the  prom- 

inent facts  and  dates,  in  fifty-three  pages.  May  be  committed  to  memory  ver- 
batim, used  in  review  of  larger  volumes,  or  for  reference  simply.  "  A  miniature 
of  American  History." 

FNRI  flNR      '•  Berard's  School   History  of  England,  combining 

LIlULHIlU"  an  interesting  history  of  the  social   life  of  the  English 

people,  with  that  of  the  civil  and  military  transactions  of  the  realm.  Religion, 
literature,  science,  art,  and  commerce  are  included. 

2.   Summary  of  English  and  of  French   History. 

A*  series  of  brief  statements,  presenting  more  points  of 

attachment  for  the  pupil's  interest  and  memory  than  a  chronological  table. 

well-proportional  outline  and  index  to  more  extended  reading. 


ROME 


Ricord's  History  of  Rome.  A  story-like  epitome  of  this  inter- 
esting  and  chivaln.  as  history,  profusely  illustrated,  with  the  legends 
and  doubtful  portions  so  introduced  as  not  to  deceive,  while  adding  extended 
charm  to  the  subject. 

HFNFRAI        Willard's  Universal   History.    A  vast  subject  BO  arranged 
UL.I1UIIHI..  and  illustrated  as  to  be  less  difficult  to  acquire  or  retain.  Its 

whole  substance,  in  fact,  is  summarized  on  one  page,  in  a  grand  '•  Temple  of 

Time,  or  Picture  of  Nations. 

2.  General  Summary  of  History.  Being  the  Summaries  of  American,  »nd 
of  English  and  French  History,  bound  in  one  volume.  The  leading  events  in 
the  histories  of  these  three  nations  epitomized  in  the  briefest  manner. 


A.   S.   BARNES   &.  CO., 


